ScaDaMaLe Course site and book

This notebook is from databricks document: - https://docs.databricks.com/_static/notebooks/package-cells.html

As you know, we need to eventually package and deploy our models, say using sbt.

However it is nice to be in a notebook environment to prototype and build intuition and create better pipelines.

Using package cells we can be in the best of both worlds to an extent.

Package Cells

Package cells are special cells that get compiled when executed. These cells have no visibility with respect to the rest of the notebook. You may think of them as separate scala files.

This means that only class and object definitions may go inside this cell. You may not have any variable or function definitions lying around by itself. The following cell will not work.

If you wish to use custom classes and/or objects defined within notebooks reliably in Spark, and across notebook sessions, you must use package cells to define those classes.

Unless you use package cells to define classes, you may also come across obscure bugs as follows:

// We define a class
case class TestKey(id: Long, str: String)
defined class TestKey
// we use that class as a key in the group by
val rdd = sc.parallelize(Array((TestKey(1L, "abd"), "dss"), (TestKey(2L, "ggs"), "dse"), (TestKey(1L, "abd"), "qrf")))

rdd.groupByKey().collect
rdd: org.apache.spark.rdd.RDD[(TestKey, String)] = ParallelCollectionRDD[0] at parallelize at command-2971213210276613:2
res0: Array[(TestKey, Iterable[String])] = Array((TestKey(1,abd),CompactBuffer(dss)), (TestKey(1,abd),CompactBuffer(qrf)), (TestKey(2,ggs),CompactBuffer(dse)))

What went wrong above? Even though we have two elements for the key TestKey(1L, "abd"), they behaved as two different keys resulting in:

Array[(TestKey, Iterable[String])] = Array(
  (TestKey(2,ggs),CompactBuffer(dse)), 
  (TestKey(1,abd),CompactBuffer(dss)), 
  (TestKey(1,abd),CompactBuffer(qrf)))

Once we define our case class within a package cell, we will not face this issue.

package com.databricks.example

case class TestKey(id: Long, str: String)
Warning: classes defined within packages cannot be redefined without a cluster restart.
Compilation successful.
import com.databricks.example

val rdd = sc.parallelize(Array(
  (example.TestKey(1L, "abd"), "dss"), (example.TestKey(2L, "ggs"), "dse"), (example.TestKey(1L, "abd"), "qrf")))

rdd.groupByKey().collect
import com.databricks.example
rdd: org.apache.spark.rdd.RDD[(com.databricks.example.TestKey, String)] = ParallelCollectionRDD[2] at parallelize at command-2971213210276616:3
res2: Array[(com.databricks.example.TestKey, Iterable[String])] = Array((TestKey(1,abd),CompactBuffer(dss, qrf)), (TestKey(2,ggs),CompactBuffer(dse)))

As you can see above, the group by worked above, grouping two elements (dss, qrf) under TestKey(1,abd).

These cells behave as individual source files, therefore only classes and objects can be defined inside these cells.

package x.y.z

val aNumber = 5 // won't work

def functionThatWillNotWork(a: Int): Int = a + 1

The following cell is the way to go.

package x.y.z

object Utils {
  val aNumber = 5 // works!
  def functionThatWillWork(a: Int): Int = a + 1
}
Warning: classes defined within packages cannot be redefined without a cluster restart.
Compilation successful.
import x.y.z.Utils

Utils.functionThatWillWork(Utils.aNumber)
import x.y.z.Utils
res5: Int = 6

Why did we get the warning: classes defined within packages cannot be redefined without a cluster restart?

Classes that get compiled with the package cells get dynamically injected into Spark's classloader. Currently it's not possible to remove classes from Spark's classloader. Any classes that you define and compile will have precedence in the classloader, therefore once you recompile, it will not be visible to your application.

Well that kind of beats the purpose of iterative notebook development if I have to restart the cluster, right? In that case, you may just rename the package to x.y.z2 during development/fast iteration and fix it once everything works.

One thing to remember with package cells is that it has no visiblity regarding the notebook environment.

  • The SparkContext will not be defined as sc.
  • The SQLContext will not be defined as sqlContext.
  • Did you import a package in a separate cell? Those imports will not be available in the package cell and have to be remade.
  • Variables imported through %run cells will not be available.

It is really a standalone file that just looks like a cell in a notebook. This means that any function that uses anything that was defined in a separate cell, needs to take that variable as a parameter or the class needs to take it inside the constructor.

package x.y.zpackage

import org.apache.spark.SparkContext

case class IntArray(values: Array[Int])

class MyClass(sc: SparkContext) {
  def sparkSum(array: IntArray): Int = {
    sc.parallelize(array.values).reduce(_ + _)
  }
}

object MyClass {
  def sparkSum(sc: SparkContext, array: IntArray): Int = {
    sc.parallelize(array.values).reduce(_ + _)
  }
}
Warning: classes defined within packages cannot be redefined without a cluster restart.
Compilation successful.
import x.y.zpackage._

val array = IntArray(Array(1, 2, 3, 4, 5))

val myClass = new MyClass(sc)
myClass.sparkSum(array)
import x.y.zpackage._
array: x.y.zpackage.IntArray = IntArray([I@44a91426)
myClass: x.y.zpackage.MyClass = x.y.zpackage.MyClass@5d3b142
res7: Int = 15
MyClass.sparkSum(sc, array)
res8: Int = 15

Build Packages Locally

Although package cells are quite handy for quick prototyping in notebook environemnts, it is better to develop packages locally on your laptop and then upload the packaged or assembled jar file into databricks to use the classes and methods developed in the package.

ScaDaMaLe Course site and book

Core ideas in Monte Carlo simulation

  • modular arithmetic gives pseudo-random streams that are indistiguishable from 'true' Uniformly distributed samples in integers from \({0,1,2,...,m}\)
  • by diving the integer streams from above by \(m\) we get samples from \({0/m,1/m,...,(m-1)/m}\) and "pretend" this to be samples from the Uniform(0,1) RV
  • we can use inverse distribution function of von Neumann's rejection sampler to convert samples from Uniform(0,1) RV to the following:
    • any other random variable
    • vector of random variables that could be dependent
    • or more generally other random structures:
      • random graphs and networks
      • random walks or (sensible perturbations of live traffic data on open street maps for hypothesis tests)
      • models of interacting paticle systems in ecology / chemcal physics, etc...
def frameIt( u:String, h:Int ) : String = {
      """<iframe 
 src=""""+ u+""""
 width="95%" height="""" + h + """"
 sandbox>
  <p>
    <a href="http://spark.apache.org/docs/latest/index.html">
      Fallback link for browsers that, unlikely, don't support frames
    </a>
  </p>
</iframe>"""
   }
displayHTML(frameIt("https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)",500))

breeze.stats.distributions

Breeze also provides a fairly large number of probability distributions. These come with access to probability density function for either discrete or continuous distributions. Many distributions also have methods for giving the mean and the variance.

import breeze.stats.distributions._

val poi = new Poisson(3.0);
import breeze.stats.distributions._
poi: breeze.stats.distributions.Poisson = Poisson(3.0)
val s = poi.sample(5); // let's draw five samples - black-box
s: IndexedSeq[Int] = Vector(2, 4, 3, 4, 6)

Getting probabilities of the Poisson samples

s.map( x => poi.probabilityOf(x) ) // PMF
res0: IndexedSeq[Double] = Vector(0.22404180765538775, 0.16803135574154085, 0.22404180765538775, 0.16803135574154085, 0.05040940672246224)
val doublePoi = for(x <- poi) yield x.toDouble // meanAndVariance requires doubles, but Poisson samples over Ints
doublePoi: breeze.stats.distributions.Rand[Double] = MappedRand(Poisson(3.0),$Lambda$5909/1062631843@70cdbd4c)
breeze.stats.meanAndVariance(doublePoi.samples.take(1000));
res1: breeze.stats.meanAndVariance.MeanAndVariance = MeanAndVariance(3.0660000000000034,3.250894894894892,1000)
(poi.mean, poi.variance) // population mean and variance
res2: (Double, Double) = (3.0,3.0)

Exponential random Variable

Let's focus on getting our hands direty with a common random variable.

NOTE: Below, there is a possibility of confusion for the term rate in the family of exponential distributions. Breeze parameterizes the distribution with the mean, but refers to it as the rate.

val expo = new Exponential(0.5);
expo: breeze.stats.distributions.Exponential = Exponential(0.5)
expo.rate // what is the rate parameter
res3: Double = 0.5

A characteristic of exponential distributions is its half-life, but we can compute the probability a value falls between any two numbers.

expo.probability(0, math.log(2) * expo.rate)
res4: Double = 0.5
expo.probability(math.log(2) * expo.rate, 10000.0)
res5: Double = 0.5
expo.probability(0.0, 1.5)
res6: Double = 0.950212931632136

The above result means that approximately 95% of the draws from an exponential distribution fall between 0 and thrice the mean. We could have easily computed this with the cumulative distribution as well.

1 - math.exp(-3.0) // the CDF of the Exponential RV with rate parameter 3
res7: Double = 0.950212931632136
val samples = expo.sample(2).sorted; // built-in black box - we will roll our own shortly in Spark
samples: IndexedSeq[Double] = Vector(2.412493444974671, 3.6802759985818687)
expo.probability(samples(0), samples(1));
res8: Double = 0.007390811722912227
breeze.stats.meanAndVariance(expo.samples.take(10000)); // mean and variance of the sample
res9: breeze.stats.meanAndVariance.MeanAndVariance = MeanAndVariance(2.0109026469746554,4.073504140726905,10000)
(1 / expo.rate, 1 / (expo.rate * expo.rate)) // mean and variance of the population
res10: (Double, Double) = (2.0,4.0)
import spark.implicits._
import org.apache.spark.sql.functions._
import spark.implicits._
import org.apache.spark.sql.functions._
val df = spark.range(1000).toDF("Id") // just make a DF of 1000 row indices
df: org.apache.spark.sql.DataFrame = [Id: bigint]
df.show(5)
+---+
| Id|
+---+
|  0|
|  1|
|  2|
|  3|
|  4|
+---+
only showing top 5 rows
val dfRand = df.select($"Id", rand(seed=1234567) as "rand") // add a column of random numbers in (0,1)
dfRand: org.apache.spark.sql.DataFrame = [Id: bigint, rand: double]
dfRand.show(5) // these are first 5 of the 1000 samples from the Uniform(0,1) RV
+---+--------------------+
| Id|                rand|
+---+--------------------+
|  0|0.024042816995877625|
|  1|  0.4763832311243641|
|  2|  0.3392911406256911|
|  3|  0.6282132043405342|
|  4|  0.9665960987271114|
+---+--------------------+
only showing top 5 rows
val dfRand = df.select($"Id", rand(seed=1234567) as "rand") // add a column of random numbers in (0,1)
dfRand.show(5) // these are first 5 of the 1000 samples from the Uniform(0,1) RV
+---+--------------------+
| Id|                rand|
+---+--------------------+
|  0|0.024042816995877625|
|  1|  0.4763832311243641|
|  2|  0.3392911406256911|
|  3|  0.6282132043405342|
|  4|  0.9665960987271114|
+---+--------------------+
only showing top 5 rows

dfRand: org.apache.spark.sql.DataFrame = [Id: bigint, rand: double]
val dfRand = df.select($"Id", rand(seed=879664) as "rand") // add a column of random numbers in (0,1)
dfRand.show(5) // these are first 5 of the 1000 samples from the Uniform(0,1) RV
+---+-------------------+
| Id|               rand|
+---+-------------------+
|  0|  0.269224348263137|
|  1|0.20433965628039852|
|  2| 0.8481228617934538|
|  3| 0.6665103087537884|
|  4| 0.7712898780552342|
+---+-------------------+
only showing top 5 rows

dfRand: org.apache.spark.sql.DataFrame = [Id: bigint, rand: double]

Let's use the inverse CDF of the Exponential RV to transform these samples from the Uniform(0,1) RV into those from the Exponential RV.

val dfRand = df.select($"Id", rand(seed=1234567) as "rand") // add a column of random numbers in (0,1)
               .withColumn("one",lit(1.0))
               .withColumn("rate",lit(0.5))
dfRand: org.apache.spark.sql.DataFrame = [Id: bigint, rand: double ... 2 more fields]
dfRand.show(5) 
+---+--------------------+---+----+
| Id|                rand|one|rate|
+---+--------------------+---+----+
|  0|0.024042816995877625|1.0| 0.5|
|  1|  0.4763832311243641|1.0| 0.5|
|  2|  0.3392911406256911|1.0| 0.5|
|  3|  0.6282132043405342|1.0| 0.5|
|  4|  0.9665960987271114|1.0| 0.5|
+---+--------------------+---+----+
only showing top 5 rows
val dfExpRand = dfRand.withColumn("expo_sample", -($"one" / $"rate") * log($"one" - $"rand")) // samples from expo(rate=0.5)
dfExpRand: org.apache.spark.sql.DataFrame = [Id: bigint, rand: double ... 3 more fields]
dfExpRand.show(5)
+---+--------------------+---+----+--------------------+
| Id|                rand|one|rate|         expo_sample|
+---+--------------------+---+----+--------------------+
|  0|0.024042816995877625|1.0| 0.5|0.048673126808362034|
|  1|  0.4763832311243641|1.0| 0.5|  1.2939904386814756|
|  2|  0.3392911406256911|1.0| 0.5|  0.8288839819270684|
|  3|  0.6282132043405342|1.0| 0.5|  1.9788694379168241|
|  4|  0.9665960987271114|1.0| 0.5|   6.798165162486205|
+---+--------------------+---+----+--------------------+
only showing top 5 rows
display(dfExpRand)
Id rand one rate expo_sample
0.0 2.4042816995877625e-2 1.0 0.5 4.8673126808362034e-2
1.0 0.4763832311243641 1.0 0.5 1.2939904386814756
2.0 0.3392911406256911 1.0 0.5 0.8288839819270684
3.0 0.6282132043405342 1.0 0.5 1.9788694379168241
4.0 0.9665960987271114 1.0 0.5 6.798165162486205
5.0 0.8269758822163711 1.0 0.5 3.508648570093974
6.0 0.3404052214826948 1.0 0.5 0.8322592089262
7.0 0.5658253891225227 1.0 0.5 1.6686169931673005
8.0 0.11737981749647353 1.0 0.5 0.24972063061386013
9.0 0.7848668745585088 1.0 0.5 3.072996508744745
10.0 0.10665116151243736 1.0 0.5 0.2255562755600773
11.0 0.34971775733163646 1.0 0.5 0.8606975816973311
12.0 3.349566781262969e-2 1.0 0.5 6.813899599567436e-2
13.0 0.334063669089834 1.0 0.5 0.8131224244912618
14.0 0.4105052702588069 1.0 0.5 1.0569789985263547
15.0 0.22519777483698333 1.0 0.5 0.5102949510683874
16.0 0.21124107883891907 1.0 0.5 0.47458910937069004
17.0 0.12332274767843698 1.0 0.5 0.26323273531964136
18.0 4.324422155449681e-2 1.0 0.5 8.841423006745963e-2
19.0 3.933267172708754e-2 1.0 0.5 8.025420479220831e-2
20.0 0.8162723223794007 1.0 0.5 3.388601261211285
21.0 7.785566240785313e-2 1.0 0.5 0.16210703862675058
22.0 0.1244015150504949 1.0 0.5 0.26569528726942954
23.0 0.5313795676534989 1.0 0.5 1.5159243018004147
24.0 0.8177063965639969 1.0 0.5 3.4042733720631824
25.0 0.7757379079578416 1.0 0.5 2.98987971469377
26.0 0.9019086568714294 1.0 0.5 4.643712323362237
27.0 0.5793202308042869 1.0 0.5 1.7317667559523853
28.0 4.913530139386124e-2 1.0 0.5 0.10076699863506142
29.0 0.6984668419742928 1.0 0.5 2.3977505839877837
30.0 1.579141234703818e-2 1.0 0.5 3.18348501444197e-2
31.0 0.3170147319677016 1.0 0.5 0.762563978285606
32.0 0.6243818511105477 1.0 0.5 1.9583644261768265
33.0 0.9720896733059052 1.0 0.5 7.157517052464175
34.0 6.406755887221727e-2 1.0 0.5 0.13242396678361196
35.0 0.8275324400058236 1.0 0.5 3.515092236401242
36.0 0.4223760255739688 1.0 0.5 1.0976643705892708
37.0 0.6237792697270514 1.0 0.5 1.9551585184791915
38.0 0.30676209726152626 1.0 0.5 0.7327640894184466
39.0 0.7209798363387625 1.0 0.5 2.5529424571699533
40.0 0.5408086036735253 1.0 0.5 1.556576340750279
41.0 0.22254408000797787 1.0 0.5 0.5034566621599345
42.0 0.6478051949133747 1.0 0.5 2.0871416658496442
43.0 0.6186563924196967 1.0 0.5 1.9281089062362353
44.0 0.2689179760895458 1.0 0.5 0.6264592354306907
45.0 0.1310898372764776 1.0 0.5 0.28103107825164747
46.0 0.8459785027719904 1.0 0.5 3.741326187841892
47.0 0.7844461581951896 1.0 0.5 3.069089109365284
48.0 0.3195541476806115 1.0 0.5 0.7700140609818293
49.0 0.326892158146161 1.0 0.5 0.7916994433570004
50.0 0.4392312327086285 1.0 0.5 1.1568932758900772
51.0 0.5377790694946909 1.0 0.5 1.543424595293625
52.0 0.4369640582174875 1.0 0.5 1.1488236262486446
53.0 0.26672242876690055 1.0 0.5 0.6204619408451196
54.0 0.9743181848790359 1.0 0.5 7.323944240755433
55.0 0.5636877255447679 1.0 0.5 1.6587941323713102
56.0 0.8214194684040824 1.0 0.5 3.44543124420649
57.0 4.2394218638494574e-2 1.0 0.5 8.663817482333575e-2
58.0 0.2986030735782996 1.0 0.5 0.7093626466953578
59.0 0.9251464009715654 1.0 0.5 5.184442172120483
60.0 0.9768531076059933 1.0 0.5 7.531789490600966
61.0 0.4147651110232632 1.0 0.5 1.0714839854387161
62.0 0.4525161010109643 1.0 0.5 1.2048444519262322
63.0 7.638776464132979e-2 1.0 0.5 0.1589259082490955
64.0 0.8203900440907219 1.0 0.5 3.433935381714252
65.0 0.9746746584977457 1.0 0.5 7.35189948830076
66.0 0.41832172801299305 1.0 0.5 1.083675562745256
67.0 3.3131200470495226e-2 1.0 0.5 6.738494114620364e-2
68.0 0.10008247055930286 1.0 0.5 0.21090430762250917
69.0 0.4268021831375646 1.0 0.5 1.113048783438383
70.0 0.8213380254753332 1.0 0.5 3.444519337826204
71.0 0.47431121070064797 1.0 0.5 1.2860917933318652
72.0 0.68679164992865 1.0 0.5 2.321773309424188
73.0 0.7057803676609208 1.0 0.5 2.4468574835462356
74.0 0.32184620342731496 1.0 0.5 0.776762356325894
75.0 0.3589329148022541 1.0 0.5 0.8892423408857425
76.0 0.7448782338623747 1.0 0.5 2.7320286670643386
77.0 0.9740613004640858 1.0 0.5 7.304038469785621
78.0 0.7453909609063684 1.0 0.5 2.736052180743762
79.0 6.853610233988816e-2 1.0 0.5 0.14199569380051374
80.0 0.336012781812836 1.0 0.5 0.8189847588182159
81.0 0.2963058480260412 1.0 0.5 0.7028229208813994
82.0 0.38627232525200883 1.0 0.5 0.9764079513820425
83.0 0.9097248909817963 1.0 0.5 4.809787008391862
84.0 0.20679745942261907 1.0 0.5 0.46335335878970363
85.0 0.16582497569469312 1.0 0.5 0.36262407472768277
86.0 0.6960738838737711 1.0 0.5 2.381941292346302
87.0 0.890094879396298 1.0 0.5 4.416275650715409
88.0 0.8258738496535992 1.0 0.5 3.4959504809275685
89.0 0.4066244237870885 1.0 0.5 1.0438554620679272
90.0 0.44414816275414526 1.0 0.5 1.1745070000344822
91.0 0.8820223175378497 1.0 0.5 4.274519608161631
92.0 0.3814200182827251 1.0 0.5 0.9606575597598919
93.0 0.491252177347836 1.0 0.5 1.3516056440673538
94.0 0.9042145561359308 1.0 0.5 4.691289097027222
95.0 0.8293982814391448 1.0 0.5 3.536847140695551
96.0 0.6957817964411346 1.0 0.5 2.38002012037681
97.0 0.46108317902841456 1.0 0.5 1.2363880819986401
98.0 0.658234439306857 1.0 0.5 2.14726054405596
99.0 0.43175037735005384 1.0 0.5 1.130388960612226
100.0 0.7719881477151886 1.0 0.5 2.9567153353469786
101.0 6.397418621476536e-2 1.0 0.5 0.13222444810891013
102.0 0.44410081132020296 1.0 0.5 1.1743366329905425
103.0 0.9364231799229901 1.0 0.5 5.511012678534471
104.0 0.5453471566845608 1.0 0.5 1.576442265948382
105.0 0.7346238968987211 1.0 0.5 2.653214404406468
106.0 0.3493365535175731 1.0 0.5 0.8595254994862054
107.0 0.5230037795263933 1.0 0.5 1.480493423321206
108.0 0.6886814284788837 1.0 0.5 2.333877090719847
109.0 0.7731252946239237 1.0 0.5 2.966714745163421
110.0 2.276168830750991e-2 1.0 0.5 4.604946957472576e-2
111.0 0.264951110753621 1.0 0.5 0.6156365319998442
112.0 0.14616140102686104 1.0 0.5 0.3160261944637388
113.0 3.066619523108849e-2 1.0 0.5 6.229248529326732e-2
114.0 0.49017052188807597 1.0 0.5 1.3473579316333943
115.0 9.835381148010536e-2 1.0 0.5 0.20706617613153588
116.0 8.828156810764243e-2 1.0 0.5 0.1848481470740138
117.0 0.6868446103815881 1.0 0.5 2.3221115183574854
118.0 0.4067862578001439 1.0 0.5 1.0444010055396156
119.0 0.44070042328022496 1.0 0.5 1.1621400679168603
120.0 0.19523663294276805 1.0 0.5 0.4344139974853618
121.0 0.34930320794183467 1.0 0.5 0.8594230049585315
122.0 0.37713232784782635 1.0 0.5 0.9468423740115679
123.0 0.6429635193876022 1.0 0.5 2.0598346316676848
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961.0 0.8460764659780871 1.0 0.5 3.7425986644134888
962.0 0.10514312394105463 1.0 0.5 0.22218297702597922
963.0 0.6975701033741791 1.0 0.5 2.3918115501203125
964.0 0.9576315406611462 1.0 0.5 6.322702154160914
965.0 0.5756726043081537 1.0 0.5 1.714499924122977
966.0 0.14180795869433915 1.0 0.5 0.3058547603470779
967.0 0.476602852426136 1.0 0.5 1.2948294774050015
968.0 0.5735933728030692 1.0 0.5 1.7047237280891907
969.0 0.21074148987963792 1.0 0.5 0.47332273812264397
970.0 0.4040283383810781 1.0 0.5 1.0351243213329395
971.0 0.44809616679520103 1.0 0.5 1.188762926181943
972.0 0.49753260138877997 1.0 0.5 1.376449039078463
973.0 0.3981895324367999 1.0 0.5 1.0156254423601343
974.0 0.4631341447354761 1.0 0.5 1.2440140393123216
975.0 0.7621220718869883 1.0 0.5 2.8719952879613677
976.0 0.35491286990322435 1.0 0.5 0.8767397717764418
977.0 0.5624416059435056 1.0 0.5 1.6530902199238997
978.0 0.9048958001682184 1.0 0.5 4.705564296273839
979.0 0.5871353426885598 1.0 0.5 1.769270891992473
980.0 0.9552974642377905 1.0 0.5 6.215450101021099
981.0 0.11683294268351829 1.0 0.5 0.24848180677799192
982.0 0.804763553103361 1.0 0.5 3.2670878135466657
983.0 0.9017746463190758 1.0 0.5 4.640981825644075
984.0 0.3546593618234335 1.0 0.5 0.8759539607786164
985.0 0.8175329055993971 1.0 0.5 3.4023708537413193
986.0 0.9271651336840998 1.0 0.5 5.239121011041082
987.0 0.43755514801054285 1.0 0.5 1.150924381235035
988.0 0.12335439229044076 1.0 0.5 0.2633049287820745
989.0 0.3823717678509384 1.0 0.5 0.9637371372795477
990.0 0.7134192888551714 1.0 0.5 2.499470136417535
991.0 0.5559806916407091 1.0 0.5 1.6237744603995141
992.0 0.7947950806945909 1.0 0.5 3.167492385499269
993.0 0.8593443260366468 1.0 0.5 3.9228808076956767
994.0 0.9695468897099642 1.0 0.5 6.983134291741286
995.0 9.645307355937993e-2 1.0 0.5 0.20285446358422873
996.0 0.5759218175673997 1.0 0.5 1.7156748964373492
997.0 0.8948271404741518 1.0 0.5 4.504300002523024
998.0 0.8288317043606008 1.0 0.5 3.5302160428926017
999.0 0.7727026977235016 1.0 0.5 2.962992833506503
dfExpRand.describe().show() // look sensible
+-------+-----------------+--------------------+----+----+--------------------+
|summary|               Id|                rand| one|rate|         expo_sample|
+-------+-----------------+--------------------+----+----+--------------------+
|  count|             1000|                1000|1000|1000|                1000|
|   mean|            499.5|  0.5060789944940257| 1.0| 0.5|   2.024647367046763|
| stddev|288.8194360957494| 0.28795893414434537| 0.0| 0.0|  1.9649069025265538|
|    min|                0|6.282087728304298E-4| 1.0| 0.5|0.001256812357281...|
|    max|              999|  0.9981606891187609| 1.0| 0.5|  12.596728597154938|
+-------+-----------------+--------------------+----+----+--------------------+
val expoSamplesDF = spark.range(1000000000).toDF("Id") // just make a DF of 100 row indices
               .select($"Id", rand(seed=1234567) as "rand") // add a column of random numbers in (0,1)
               .withColumn("one",lit(1.0))
               .withColumn("rate",lit(0.5))
               .withColumn("expo_sample", -($"one" / $"rate") * log($"one" - $"rand"))
expoSamplesDF: org.apache.spark.sql.DataFrame = [Id: bigint, rand: double ... 3 more fields]
expoSamplesDF.describe().show()
+-------+--------------------+--------------------+----------+----------+--------------------+
|summary|                  Id|                rand|       one|      rate|         expo_sample|
+-------+--------------------+--------------------+----------+----------+--------------------+
|  count|          1000000000|          1000000000|1000000000|1000000000|          1000000000|
|   mean|4.9999999907595944E8| 0.49999521358240573|       1.0|       0.5|  1.9999814119383708|
| stddev|2.8867513473915565E8|  0.2886816216562552|       0.0|       0.0|  2.0000011916404206|
|    min|                   0|1.584746778249268...|       1.0|       0.5|3.169493556749679...|
|    max|           999999999|  0.9999999996809935|       1.0|       0.5|  43.731619350261035|
+-------+--------------------+--------------------+----------+----------+--------------------+

Approximating Pi with Monte Carlo simulations

Uisng RDDs directly, let's estimate Pi.

//Calculate pi with Monte Carlo estimation
import scala.math.random

//make a very large unique set of 1 -> n 
val partitions = 2 
val n = math.min(100000L * partitions, Int.MaxValue).toInt 
val xs = 1 until n 

//split up n into the number of partitions we can use 
val rdd = sc.parallelize(xs, partitions).setName("'N values rdd'")

//generate a random set of points within a 2x2 square
val sample = rdd.map { i =>
  val x = random * 2 - 1
  val y = random * 2 - 1
  (x, y)
}.setName("'Random points rdd'")

//points w/in the square also w/in the center circle of r=1
val inside = sample.filter { case (x, y) => (x * x + y * y < 1) }.setName("'Random points inside circle'")
val count = inside.count()
 
//Area(circle)/Area(square) = inside/n => pi=4*inside/n                        
println("Pi is roughly " + 4.0 * count / n)
Pi is roughly 3.14156
import scala.math.random
partitions: Int = 2
n: Int = 200000
xs: scala.collection.immutable.Range = Range 1 until 200000
rdd: org.apache.spark.rdd.RDD[Int] = 'N values rdd' ParallelCollectionRDD[39] at parallelize at command-2971213210276568:10
sample: org.apache.spark.rdd.RDD[(Double, Double)] = 'Random points rdd' MapPartitionsRDD[40] at map at command-2971213210276568:13
inside: org.apache.spark.rdd.RDD[(Double, Double)] = 'Random points inside circle' MapPartitionsRDD[41] at filter at command-2971213210276568:20
count: Long = 157078

Doing it in PySpark is just as easy. This may be needed if there are pyhton libraries you want to take advantage of in Spark.

# # Estimating $\pi$
#
# This PySpark example shows you how to estimate $\pi$ in parallel
# using Monte Carlo integration.

from __future__ import print_function
import sys
from random import random
from operator import add

partitions = 2
n = 100000 * partitions

def f(_):
    x = random() * 2 - 1
    y = random() * 2 - 1
    return 1 if x ** 2 + y ** 2 < 1 else 0

# To access the associated SparkContext
count = spark.sparkContext.parallelize(range(1, n + 1), partitions).map(f).reduce(add)
print("Pi is roughly %f" % (4.0 * count / n))
Pi is roughly 3.138820

The following is from this google turotial.

Programming a Monte Carlo simulation in Scala

Monte Carlo, of course, is famous as a gambling destination. In this section, you use Scala to create a simulation that models the mathematical advantage that a casino enjoys in a game of chance. The "house edge" at a real casino varies widely from game to game; it can be over 20% in keno, for example. This tutorial creates a simple game where the house has only a one-percent advantage. Here's how the game works:

  1. The player places a bet, consisting of a number of chips from a bankroll fund.
  • The player rolls a 100-sided die (how cool would that be?).
  • If the result of the roll is a number from 1 to 49, the player wins.
  • For results 50 to 100, the player loses the bet.

You can see that this game creates a one-percent disadvantage for the player: in 51 of the 100 possible outcomes for each roll, the player loses.

Follow these steps to create and run the game:

val STARTING_FUND = 10
val STAKE = 1   // the amount of the bet
val NUMBER_OF_GAMES = 25

def rollDie: Int = {
    val r = scala.util.Random
    r.nextInt(99) + 1
}

def playGame(stake: Int): (Int) = {
    val faceValue = rollDie
    if (faceValue < 50)
        (2*stake)
    else
        (0)
}

// Function to play the game multiple times
// Returns the final fund amount
def playSession(
   startingFund: Int = STARTING_FUND,
   stake: Int = STAKE,
   numberOfGames: Int = NUMBER_OF_GAMES):
   (Int) = {

    // Initialize values
    var (currentFund, currentStake, currentGame) = (startingFund, 0, 1)

    // Keep playing until number of games is reached or funds run out
    while (currentGame <= numberOfGames && currentFund > 0) {

        // Set the current bet and deduct it from the fund
        currentStake = math.min(stake, currentFund)
        currentFund -= currentStake

        // Play the game
        val (winnings) = playGame(currentStake)

        // Add any winnings
        currentFund += winnings

        // Increment the loop counter
        currentGame += 1
    }
    (currentFund)
}
STARTING_FUND: Int = 10
STAKE: Int = 1
NUMBER_OF_GAMES: Int = 25
rollDie: Int
playGame: (stake: Int)Int
playSession: (startingFund: Int, stake: Int, numberOfGames: Int)Int

Enter the following code to play the game 25 times, which is the default value for NUMBER_OF_GAMES.

playSession()
res31: Int = 5

Your bankroll started with a value of 10 units. Is it higher or lower, now?

Now simulate 10,000 players betting 100 chips per game. Play 10,000 games in a session. This Monte Carlo simulation calculates the probability of losing all your money before the end of the session. Enter the follow code:

(sc.parallelize(1 to 10000, 500)
  .map(i => playSession(100000, 100, 250000))
  .map(i => if (i == 0) 1 else 0)
  .reduce(_+_)/10000.0)
res32: Double = 0.9992

Note that the syntax .reduce(_+_) is shorthand in Scala for aggregating by using a summing function.

The preceding code performs the following steps:

  1. Creates an RDD with the results of playing the session.
  • Replaces bankrupt players' results with the number 1 and nonzero results with the number 0.
  • Sums the count of bankrupt players.
  • Divides the count by the number of players.

A typical result might be:

res32: Double = 0.9992

Which represents a near guarantee of losing all your money, even though the casino had only a one-percent advantage.

Project Ideas

Try to create a scalable simulation of interest to you.

Here are some mature projects:

  • https://github.com/zishanfu/GeoSparkSim
  • https://github.com/srbaird/mc-var-spark

See a more complete VaR modeling: - https://databricks.com/blog/2020/05/27/modernizing-risk-management-part-1-streaming-data-ingestion-rapid-model-development-and-monte-carlo-simulations-at-scale.html

ScaDaMaLe Course site and book

Introduction to Machine Learning

Some very useful resources we will weave around for Statistical Learning, Data Mining, Machine Learning:

Deep Learning is a very popular method currently (2017) in Machine Learning and I recommend Andrew Ng's free course in Courseera for this if you have not taken a course in deep learning already.

Note: This is an applied course in data science and we will quickly move to doing things with data. You have to do work to get a deeper mathematical understanding or take other courses. We will focus on intution here and the distributed ML Pipeline in action.

I am assuming several of you have or are taking ML courses. In this course we will focus on getting our hads dirty quickly with some level of common understanding across all the disciplines represented here. Please dive deep at your own time to desired depths and tangents based on your background.

Summary of Machine Learning at a High Level

  • A rough definition of machine learning.
    • constructing and studying algorithms that learn from and make predictions on data.
  • This broad area involves tools and ideas from various domains, including:
    • computer science,
    • probability and statistics,
    • optimization,
    • linear algebra
    • logic
    • etc.
  • Common examples of ML, include:
    • facial recognition,
    • link prediction,
    • text or document classification, eg.::
      • spam detection,
    • protein structure prediction
    • teaching computers to play games (go!)

Some common terminology

using example of spam detection as a running example.
  • the data points we learn from are call observations:

    • they are items or entities used for::
      • learning or
      • evaluation.
  • in the context of spam detection,

    • emails are our observations.
    • Features are attributes used to represent an observation.
    • Features are typically numeric,
      • and in spam detection, they can be:
      • the length,
      • the date, or
      • the presence or absence of keywords in emails.
    • Labels are values or categories assigned to observations.
      • and in spam detection, they can be:
      • an email being defined as spam or not spam.
  • Training and test data sets are the observations that we use to train and evaluate a learning algorithm.

  • Pop-Quiz

    • What is the difference between supervised and unsupervised learning?

ML Pipelines

Here we will use ML Pipelines to do machine learning at scale.

See https://spark.apache.org/docs/latest/ml-pipeline.html for a quick overview.

Read this section for an overview:

ScaDaMaLe Course site and book

Million Song Dataset - Kaggle Challenge

Predict which songs a user will listen to.

SOURCE: This is just a Scala-rification of the Python notebook published in databricks community edition in 2016.

When you first hear a song, do you ever categorize it as slow or fast in your head? Is it even a valid categorization? If so, can one do it automatically? I have always wondered about that. That is why I got excited when I learned about the Million Songs Dataset -Kaggle Challenge.

In this tutorial we will walk through a practical example of a data science project with Apache Spark in Python. We are going to parse, explore and model a sample from the million songs dataset stored on distributed storage. This tutorial is organized into three sections:

  1. ETL: Parses raw texts and creates a cached table
  2. Explore: Explores different aspects of the songs table using graphs
  3. Model: Uses SparkML to cluster songs based on some of their attributes

End to End Data Science

The goal of this tutorial is to prepare you for real world data science projects. Make sure you go through the tutorial in the above order and use the exercises to make yourself familiar further with the API. Also make sure you run these notebooks on a 1.6.x cluster.

1. ETL

The first step of most data science projects is extracting, transforming and loading data into well formated tables. Our example starts with ETL as well. By following the ETL noteboook you can expect to learn about following Spark concepts:

  • RDD: Resilient Distributed Dataset
  • Reading and transforming RDDs
  • Schema in Spark
  • Spark DataFrame
  • Temp tables
  • Caching tables

2. Explore

Exploratory analysis is a key step in any real data project. Data scientists use variety of tools to explore and visualize their data. In the second notebook of this tutorial we introduce several tools in Python and Databricks notebooks that can help you visually explore your large data. By reading this notebook and finishing its exercises you will become familiar with:

  • How to view the schema of a table
  • How to display ggplot and matplotlib figures in Notebooks
  • How to summarize and visualize different aspects of large datasets
  • How to sample and visualize large data

3. Model

The end goal of many data scientists is producing useful models. These models are often used for prediction of new and upcoming events in production. In our third notebook we construct a simple K-means clustering model. In this notebook you will learn about:

  • Feature transformation
  • Fitting a model using SparkML API
  • Applying a model to data
  • Visualizing model results
  • Model tuning

013_UnsupervisedClustering_1MSongsKMeans_Stage1ETL

ScaDaMaLe Course site and book

Million Song Dataset - Kaggle Challenge

Predict which songs a user will listen to.

SOURCE: This is just a Scala-rification of the Python notebook published in databricks community edition in 2016.

Stage 2: Exploring songs data

Explore

This is the second notebook in this tutorial. In this notebook we do what any data scientist does with their data right after parsing it: exploring and understanding different aspect of data. Make sure you understand how we get the songsTable by reading and running the ETL notebook. In the ETL notebook we created and cached a temporary table named songsTable

// Let's quickly do everything to register the tempView of the table here

// fill in comment ... EXERCISE!
case class Song(artist_id: String, artist_latitude: Double, artist_longitude: Double, artist_location: String, artist_name: String, duration: Double, end_of_fade_in: Double, key: Int, key_confidence: Double, loudness: Double, release: String, song_hotness: Double, song_id: String, start_of_fade_out: Double, tempo: Double, time_signature: Double, time_signature_confidence: Double, title: String, year: Double, partial_sequence: Int)

def parseLine(line: String): Song = {
  // fill in comment ...
  
  def toDouble(value: String, defaultVal: Double): Double = {
    try {
       value.toDouble
    } catch {
      case e: Exception => defaultVal
    }
  }

  def toInt(value: String, defaultVal: Int): Int = {
    try {
       value.toInt
      } catch {
      case e: Exception => defaultVal
    }
  }
  // fill in comment ...
  val tokens = line.split("\t")
  Song(tokens(0), toDouble(tokens(1), 0.0), toDouble(tokens(2), 0.0), tokens(3), tokens(4), toDouble(tokens(5), 0.0), toDouble(tokens(6), 0.0), toInt(tokens(7), -1), toDouble(tokens(8), 0.0), toDouble(tokens(9), 0.0), tokens(10), toDouble(tokens(11), 0.0), tokens(12), toDouble(tokens(13), 0.0), toDouble(tokens(14), 0.0), toDouble(tokens(15), 0.0), toDouble(tokens(16), 0.0), tokens(17), toDouble(tokens(18), 0.0), toInt(tokens(19), -1))
}

// this is loads all the data - a subset of the 1M songs dataset
val dataRDD = sc.textFile("/datasets/sds/songs/data-001/part-*") 

// .. fill in comment
val df = dataRDD.map(parseLine).toDF

// .. fill in comment
df.createOrReplaceTempView("songsTable")
defined class Song
parseLine: (line: String)Song
dataRDD: org.apache.spark.rdd.RDD[String] = /databricks-datasets/songs/data-001/part-* MapPartitionsRDD[81] at textFile at command-2971213210276755:30
df: org.apache.spark.sql.DataFrame = [artist_id: string, artist_latitude: double ... 18 more fields]
spark.catalog.listTables.show(false) // make sure the temp view of our table is there
+----------------------------+--------+-----------+---------+-----------+
|name                        |database|description|tableType|isTemporary|
+----------------------------+--------+-----------+---------+-----------+
|countrycodes                |default |null       |EXTERNAL |false      |
|ltcar_locations_2_csv       |default |null       |MANAGED  |false      |
|magellan                    |default |null       |MANAGED  |false      |
|mobile_sample               |default |null       |EXTERNAL |false      |
|over300all_2_txt            |default |null       |MANAGED  |false      |
|person                      |default |null       |MANAGED  |false      |
|persons                     |default |null       |MANAGED  |false      |
|social_media_usage          |default |null       |MANAGED  |false      |
|social_media_usage_csv_gui  |default |null       |MANAGED  |false      |
|voronoi20191213uppsla1st_txt|default |null       |MANAGED  |false      |
|voronoi20191213uppsla2d_txt |default |null       |MANAGED  |false      |
|voronoi20191213uppsla3d_txt |default |null       |MANAGED  |false      |
|songstable                  |null    |null       |TEMPORARY|true       |
+----------------------------+--------+-----------+---------+-----------+

A first inspection

A first step to any data exploration is viewing sample data. For this purpose we can use a simple SQL query that returns first 10 rows.

select * from songsTable limit 10
artist_id artist_latitude artist_longitude artist_location artist_name duration end_of_fade_in key key_confidence loudness release song_hotness song_id start_of_fade_out tempo time_signature time_signature_confidence title year partial_sequence
AR81V6H1187FB48872 0.0 0.0 Earl Sixteen 213.7073 0.0 11.0 0.419 -12.106 Soldier of Jah Army 0.0 SOVNZSZ12AB018A9B8 208.289 125.882 1.0 0.0 Rastaman 2003.0 -1.0
ARVVZQP11E2835DBCB 0.0 0.0 Wavves 133.25016 0.0 0.0 0.282 0.596 Wavvves 0.471578247701 SOJTQHQ12A8C143C5F 128.116 89.519 1.0 0.0 I Want To See You (And Go To The Movies) 2009.0 -1.0
ARFG9M11187FB3BBCB 0.0 0.0 Nashua USA C-Side 247.32689 0.0 9.0 0.612 -4.896 Santa Festival Compilation 2008 vol.1 0.0 SOAJSQL12AB0180501 242.196 171.278 5.0 1.0 Loose on the Dancefloor 0.0 225261.0
ARK4Z2O1187FB45FF0 0.0 0.0 Harvest 337.05751 0.247 4.0 0.46 -9.092 Underground Community 0.0 SOTDRVW12AB018BEB9 327.436 84.986 4.0 0.673 No Return 0.0 101619.0
AR4VQSG1187FB57E18 35.25082 -91.74015 Searcy, AR Gossip 430.23628 0.0 2.0 3.4e-2 -6.846 Yr Mangled Heart 0.0 SOTVOCL12A8AE478DD 424.06 121.998 4.0 0.847 Yr Mangled Heart 2006.0 740623.0
ARNBV1X1187B996249 0.0 0.0 Alex 186.80118 0.0 4.0 0.641 -16.108 Jolgaledin 0.0 SODTGRY12AB0182438 166.156 140.735 4.0 5.5e-2 Mariu Sonur Jesus 0.0 673970.0
ARXOEZX1187B9B82A1 0.0 0.0 Elie Attieh 361.89995 0.0 7.0 0.863 -4.919 ELITE 0.0 SOIINTJ12AB0180BA6 354.476 128.024 4.0 0.399 Fe Yom We Leila 0.0 280304.0
ARXPUIA1187B9A32F1 0.0 0.0 Rome, Italy Simone Cristicchi 220.00281 2.119 4.0 0.486 -6.52 Dall'Altra Parte Del Cancello 0.484225272411 SONHXJK12AAF3B5290 214.761 99.954 1.0 0.928 L'Italiano 2007.0 745962.0
ARNPPTH1187B9AD429 51.4855 -0.37196 Heston, Middlesex, England Jimmy Page 156.86485 0.334 7.0 0.493 -9.962 No Introduction Necessary [Deluxe Edition] 0.0 SOGUHGW12A58A80E06 149.269 162.48 4.0 0.534 Wailing Sounds 2004.0 599250.0
AROGWRA122988FEE45 0.0 0.0 Christos Dantis 256.67873 2.537 9.0 0.742 -13.404 Daktilika Apotipomata 0.0 SOJJOYI12A8C13399D 248.912 134.944 4.0 0.162 Stin Proigoumeni Zoi 0.0 611396.0
table("songsTable").printSchema()
root
 |-- artist_id: string (nullable = true)
 |-- artist_latitude: double (nullable = false)
 |-- artist_longitude: double (nullable = false)
 |-- artist_location: string (nullable = true)
 |-- artist_name: string (nullable = true)
 |-- duration: double (nullable = false)
 |-- end_of_fade_in: double (nullable = false)
 |-- key: integer (nullable = false)
 |-- key_confidence: double (nullable = false)
 |-- loudness: double (nullable = false)
 |-- release: string (nullable = true)
 |-- song_hotness: double (nullable = false)
 |-- song_id: string (nullable = true)
 |-- start_of_fade_out: double (nullable = false)
 |-- tempo: double (nullable = false)
 |-- time_signature: double (nullable = false)
 |-- time_signature_confidence: double (nullable = false)
 |-- title: string (nullable = true)
 |-- year: double (nullable = false)
 |-- partial_sequence: integer (nullable = false)
select count(*) from songsTable
count(1)
31369.0
table("songsTable").count() // or equivalently with DataFrame API - recall table("songsTable") is a DataFrame
res4: Long = 31369
display(sqlContext.sql("SELECT duration, year FROM songsTable")) // Aggregation is set to 'Average' in 'Plot Options'
duration year
213.7073 2003.0
133.25016 2009.0
247.32689 0.0
337.05751 0.0
430.23628 2006.0
186.80118 0.0
361.89995 0.0
220.00281 2007.0
156.86485 2004.0
256.67873 0.0
204.64281 0.0
112.48281 0.0
170.39628 0.0
215.95383 0.0
303.62077 0.0
266.60526 0.0
326.19057 1997.0
51.04281 2009.0
129.4624 0.0
253.33506 2003.0
237.76608 2004.0
132.96281 0.0
399.35955 2006.0
168.75057 1991.0
396.042 0.0
192.10404 1968.0
12.2771 2006.0
367.56853 0.0
189.93587 0.0
233.50812 0.0
462.68036 0.0
202.60526 0.0
241.52771 0.0
275.64363 1992.0
350.69342 2007.0
166.55628 1968.0
249.49506 1983.0
53.86404 1992.0
233.76934 2001.0
275.12118 2009.0
191.13751 2006.0
299.07546 0.0
468.74077 0.0
110.34077 0.0
234.78812 2003.0
705.25342 2006.0
383.52934 0.0
196.10077 0.0
299.20608 1998.0
94.04036 0.0
28.08118 2006.0
207.93424 2006.0
152.0322 1999.0
207.96036 2002.0
371.25179 0.0
288.93995 2002.0
235.93751 2004.0
505.70404 0.0
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160.07791 2007.0
327.70567 0.0
174.86322 0.0
272.92689 2005.0
251.53261 0.0
216.99873 0.0
195.3171 0.0
247.11791 0.0
101.3024 0.0
315.97669 2003.0
449.67138 0.0
173.16526 1998.0
394.44853 0.0
226.69016 2007.0
219.11465 0.0
240.92689 1997.0
227.91791 1999.0
119.84934 0.0
109.92281 1997.0
116.08771 0.0
187.71546 1975.0
191.65995 0.0
116.32281 1979.0
482.45506 0.0
262.71302 2003.0
208.97914 2005.0
209.81506 1975.0
129.85424 2002.0
219.0624 0.0
500.4273 2010.0
224.7571 0.0
274.85995 2003.0
145.162 1993.0
211.27791 0.0
167.49669 1981.0
415.7122 0.0
346.33098 0.0
399.69914 1999.0
136.56771 0.0

Exercises

  1. Why do you think average song durations increase dramatically in 70's?
  2. Add error bars with standard deviation around each average point in the plot.
  3. How did average loudness change over time?
  4. How did tempo change over time?
  5. What other aspects of songs can you explore with this technique?

Sampling and visualizing

You can dive deep into Scala visualisations here: - https://docs.databricks.com/notebooks/visualizations/charts-and-graphs-scala.html

You can also use R and Python for visualisations in the same notebook: - https://docs.databricks.com/notebooks/visualizations/index.html

ScaDaMaLe Course site and book

Million Song Dataset - Kaggle Challenge

Predict which songs a user will listen to.

SOURCE: This is just a Scala-rification of the Python notebook published in databricks community edition in 2016.

Stage 3: Modeling Songs via k-means

Model

This is the third step into our project. In the first step we parsed raw text files and created a table. Then we explored different aspects of data and learned that things have been changing over time. In this step we attempt to gain deeper understanding of our data by categorizing (a.k.a. clustering) our data. For the sake of training we pick a fairly simple model based on only three parameters. We leave more sophisticated modeling as exercies to the reader

We pick the most commonly used and simplest clustering algorithm (KMeans) for our job. The SparkML KMeans implementation expects input in a vector column. Fortunately, there are already utilities in SparkML that can help us convert existing columns in our table to a vector field. It is called VectorAssembler. Here we import that functionality and use it to create a new DataFrame

// Let's quickly do everything to register the tempView of the table here

// this is a case class for our row objects
case class Song(artist_id: String, artist_latitude: Double, artist_longitude: Double, artist_location: String, artist_name: String, duration: Double, end_of_fade_in: Double, key: Int, key_confidence: Double, loudness: Double, release: String, song_hotness: Double, song_id: String, start_of_fade_out: Double, tempo: Double, time_signature: Double, time_signature_confidence: Double, title: String, year: Double, partial_sequence: Int)

def parseLine(line: String): Song = {
  // this is robust parsing by try-catching type exceptions
  
  def toDouble(value: String, defaultVal: Double): Double = {
    try {
       value.toDouble
    } catch {
      case e: Exception => defaultVal
    }
  }

  def toInt(value: String, defaultVal: Int): Int = {
    try {
       value.toInt
      } catch {
      case e: Exception => defaultVal
    }
  }
  // splitting the sting of each line by the delimiter TAB character '\t'
  val tokens = line.split("\t")
  
  // making song objects
  Song(tokens(0), toDouble(tokens(1), 0.0), toDouble(tokens(2), 0.0), tokens(3), tokens(4), toDouble(tokens(5), 0.0), toDouble(tokens(6), 0.0), toInt(tokens(7), -1), toDouble(tokens(8), 0.0), toDouble(tokens(9), 0.0), tokens(10), toDouble(tokens(11), 0.0), tokens(12), toDouble(tokens(13), 0.0), toDouble(tokens(14), 0.0), toDouble(tokens(15), 0.0), toDouble(tokens(16), 0.0), tokens(17), toDouble(tokens(18), 0.0), toInt(tokens(19), -1))
}

// this is loads all the data - a subset of the 1M songs dataset
val dataRDD = sc.textFile("/datasets/sds/songs/data-001/part-*") 

// .. fill in comment
val df = dataRDD.map(parseLine).toDF

// .. fill in comment
df.createOrReplaceTempView("songsTable")
defined class Song
parseLine: (line: String)Song
dataRDD: org.apache.spark.rdd.RDD[String] = /databricks-datasets/songs/data-001/part-* MapPartitionsRDD[106] at textFile at command-2971213210277067:32
df: org.apache.spark.sql.DataFrame = [artist_id: string, artist_latitude: double ... 18 more fields]
import org.apache.spark.ml.feature.VectorAssembler

val trainingData = new VectorAssembler()
                      .setInputCols(Array("duration", "tempo", "loudness"))
                      .setOutputCol("features")
                      .transform(table("songsTable"))
import org.apache.spark.ml.feature.VectorAssembler
trainingData: org.apache.spark.sql.DataFrame = [artist_id: string, artist_latitude: double ... 19 more fields]

All we have done above with the VectorAssembler method is:

  • created a DataFrame called trainingData
  • that transformed our table called songsTable
  • by adding an output column named features using setOutputCol("features")
  • that was obtained from an Array of the songsTable's columns named duration, tempo and loudness using
    • setInputCols(Array("duration", "tempo", "loudness")).
trainingData.take(3) // see first 3 rows of trainingData DataFrame, notice the vectors in the last column
res3: Array[org.apache.spark.sql.Row] = Array([AR81V6H1187FB48872,0.0,0.0,,Earl Sixteen,213.7073,0.0,11,0.419,-12.106,Soldier of Jah Army,0.0,SOVNZSZ12AB018A9B8,208.289,125.882,1.0,0.0,Rastaman,2003.0,-1,[213.7073,125.882,-12.106]], [ARVVZQP11E2835DBCB,0.0,0.0,,Wavves,133.25016,0.0,0,0.282,0.596,Wavvves,0.471578247701,SOJTQHQ12A8C143C5F,128.116,89.519,1.0,0.0,I Want To See You (And Go To The Movies),2009.0,-1,[133.25016,89.519,0.596]], [ARFG9M11187FB3BBCB,0.0,0.0,Nashua USA,C-Side,247.32689,0.0,9,0.612,-4.896,Santa Festival Compilation 2008 vol.1,0.0,SOAJSQL12AB0180501,242.196,171.278,5.0,1.0,Loose on the Dancefloor,0.0,225261,[247.32689,171.278,-4.896]])

Transformers

A Transformer is an abstraction that includes feature transformers and learned models. Technically, a Transformer implements a method transform(), which converts one DataFrame into another, generally by appending one or more columns. For example:

  • A feature transformer might take a DataFrame, read a column (e.g., text), map it into a new column (e.g., feature vectors), and output a new DataFrame with the mapped column appended.
  • A learning model might take a DataFrame, read the column containing feature vectors, predict the label for each feature vector, and output a new DataFrame with predicted labels appended as a column.

Estimators

An Estimator abstracts the concept of a learning algorithm or any algorithm that fits or trains on data.

Technically, an Estimator implements a method fit(), which accepts a DataFrame and produces a Model, which is a Transformer.

For example, a learning algorithm such as LogisticRegression is an Estimator, and calling fit() trains a LogisticRegressionModel, which is a Model and hence a Transformer.

display(trainingData.select("duration", "tempo", "loudness", "features").limit(5)) // see features in more detail

Demonstration of the standard algorithm

(1) (2) (3) (4)

  1. k initial "means" (in this case k=3) are randomly generated within the data domain (shown in color).
  • k clusters are created by associating every observation with the nearest mean. The partitions here represent the Voronoi diagram generated by the means.
  • The centroid of each of the k clusters becomes the new mean.
  • Steps 2 and 3 are repeated until local convergence has been reached.

The "assignment" step 2 is also referred to as expectation step, the "update step" 3 as maximization step, making this algorithm a variant of the generalized expectation-maximization algorithm.

Caveats: As k-means is a heuristic algorithm, there is no guarantee that it will converge to the global optimum, and the result may depend on the initial clusters. As the algorithm is usually very fast, it is common to run it multiple times with different starting conditions. However, in the worst case, k-means can be very slow to converge. For more details see https://en.wikipedia.org/wiki/K-means_clustering that is also embedded in-place below.

CAUTION!

Iris flower data set, clustered using

  • k-means (left) and
  • true species in the data set (right).

k-means clustering result for the Iris flower data set and actual species visualized using ELKI. Cluster means are marked using larger, semi-transparent symbols.

Note that k-means is non-determinicstic, so results vary. Cluster means are visualized using larger, semi-transparent markers. The visualization was generated using ELKI.

With some cautionary tales we go ahead with applying k-means to our dataset next.

We can now pass this new DataFrame to the KMeans model and ask it to categorize different rows in our data to two different classes (setK(2)). We place the model in a immutable value named model.

Note: This command performs multiple spark jobs (one job per iteration in the KMeans algorithm). You will see the progress bar starting over and over again.

import org.apache.spark.ml.clustering.KMeans
val model = new KMeans().setK(2).fit(trainingData) // 37 seconds in 5 workers cluster
import org.apache.spark.ml.clustering.KMeans
model: org.apache.spark.ml.clustering.KMeansModel = KMeansModel: uid=kmeans_a1617b1902bd, k=2, distanceMeasure=euclidean, numFeatures=3
//model. // uncomment and place cursor next to . and hit Tab to see all methods on model
model.clusterCenters // get cluster centres
res5: Array[org.apache.spark.ml.linalg.Vector] = Array([208.72069181761955,124.38376303683947,-9.986137113920133], [441.1413218945455,123.00973381818183,-10.560375818181816])
val modelTransformed = model.transform(trainingData) // to get predictions as last column
modelTransformed: org.apache.spark.sql.DataFrame = [artist_id: string, artist_latitude: double ... 20 more fields]

Remember that ML Pipelines works with DataFrames. So, our trainingData and modelTransformed are both DataFrames

trainingData.printSchema
root
 |-- artist_id: string (nullable = true)
 |-- artist_latitude: double (nullable = false)
 |-- artist_longitude: double (nullable = false)
 |-- artist_location: string (nullable = true)
 |-- artist_name: string (nullable = true)
 |-- duration: double (nullable = false)
 |-- end_of_fade_in: double (nullable = false)
 |-- key: integer (nullable = false)
 |-- key_confidence: double (nullable = false)
 |-- loudness: double (nullable = false)
 |-- release: string (nullable = true)
 |-- song_hotness: double (nullable = false)
 |-- song_id: string (nullable = true)
 |-- start_of_fade_out: double (nullable = false)
 |-- tempo: double (nullable = false)
 |-- time_signature: double (nullable = false)
 |-- time_signature_confidence: double (nullable = false)
 |-- title: string (nullable = true)
 |-- year: double (nullable = false)
 |-- partial_sequence: integer (nullable = false)
 |-- features: vector (nullable = true)
modelTransformed.printSchema
root
 |-- artist_id: string (nullable = true)
 |-- artist_latitude: double (nullable = false)
 |-- artist_longitude: double (nullable = false)
 |-- artist_location: string (nullable = true)
 |-- artist_name: string (nullable = true)
 |-- duration: double (nullable = false)
 |-- end_of_fade_in: double (nullable = false)
 |-- key: integer (nullable = false)
 |-- key_confidence: double (nullable = false)
 |-- loudness: double (nullable = false)
 |-- release: string (nullable = true)
 |-- song_hotness: double (nullable = false)
 |-- song_id: string (nullable = true)
 |-- start_of_fade_out: double (nullable = false)
 |-- tempo: double (nullable = false)
 |-- time_signature: double (nullable = false)
 |-- time_signature_confidence: double (nullable = false)
 |-- title: string (nullable = true)
 |-- year: double (nullable = false)
 |-- partial_sequence: integer (nullable = false)
 |-- features: vector (nullable = true)
 |-- prediction: integer (nullable = false)
  • The column features that we specified as output column to our VectorAssembler contains the features
  • The new column prediction in modelTransformed contains the predicted output
val transformed = modelTransformed.select("duration", "tempo", "loudness", "prediction")
transformed: org.apache.spark.sql.DataFrame = [duration: double, tempo: double ... 2 more fields]

To comfortably visualize the data we produce a random sample. Remember the display() function? We can use it to produce a nicely rendered table of transformed DataFrame.

// just sampling the fraction 0.005 of all the rows at random, 
// 'false' argument to sample is for sampling without replacement
display(transformed.sample(false, fraction = 0.005, 12988934L)) 
duration tempo loudness prediction
265.97832 129.987 -5.065 0.0
306.36363 127.529 -8.273 0.0
195.73506 115.191 -6.327 0.0
257.82812 92.892 -13.621 0.0
177.55383 149.853 -10.969 0.0
224.9922 97.98 -5.921 0.0
528.09098 160.022 -5.956 1.0
213.68118 100.219 -4.528 0.0
35.52608 121.349 -18.721 0.0
213.68118 120.581 -10.633 0.0
300.53832 139.017 -13.319 0.0
138.81424 160.044 -11.138 0.0
413.962 89.588 -13.143 1.0
292.17914 188.543 -5.389 0.0
419.34322 140.008 -5.389 1.0
261.61587 152.951 -12.447 0.0
168.64608 99.617 -8.164 0.0
446.27546 196.005 -6.621 1.0
343.92771 122.877 -10.264 1.0
261.69424 145.129 -4.733 0.0
408.47628 61.259 -11.244 1.0
243.3824 161.778 -6.88 0.0
184.00608 111.461 -9.788 0.0
67.39546 188.723 -3.239 0.0
165.51138 81.125 -18.692 0.0
214.85669 144.174 -17.989 0.0
185.96526 186.897 -6.041 0.0
170.05669 75.356 -16.486 0.0
193.72363 117.131 -9.822 0.0
227.23873 91.953 -11.221 0.0
177.6322 150.962 -7.288 0.0
117.21098 100.021 -10.782 0.0
422.42567 91.214 -8.872 1.0
145.162 95.388 -10.166 0.0
242.93832 112.015 -7.135 0.0
366.00118 65.05 -13.768 1.0
601.15546 70.623 -11.179 1.0
196.17914 121.563 -5.434 0.0
399.35955 124.963 -3.415 1.0
287.73832 161.648 -14.721 0.0
285.09995 132.86 -10.23 0.0
358.32118 132.874 -6.071 1.0
407.71873 85.996 -10.103 1.0
463.25506 95.083 -6.4 1.0
295.91465 93.515 -8.987 0.0
273.8673 190.044 -10.556 0.0
280.73751 113.363 -6.893 0.0
142.65424 206.067 -7.996 0.0
197.38077 84.023 -10.964 0.0
226.24608 166.768 -5.941 0.0
152.47628 153.528 -7.393 0.0
315.32363 139.919 -7.438 0.0
329.03791 180.059 -6.473 1.0
296.88118 137.976 -5.49 0.0
250.77506 84.543 -18.058 0.0
48.14322 52.814 -11.617 0.0
290.16771 141.24 -14.009 0.0
406.04689 133.997 -9.685 1.0
124.57751 161.237 -12.314 0.0
280.45016 154.003 -8.094 0.0
472.31955 219.371 -6.08 1.0
267.4673 152.123 -18.457 0.0
216.21506 88.022 -7.096 0.0
31.00689 237.737 -11.538 0.0
283.21914 132.934 -11.153 0.0
284.21179 110.585 -15.384 0.0
154.87955 157.881 -4.377 0.0
431.46404 113.905 -8.651 1.0
215.87546 124.572 -7.67 0.0
161.43628 43.884 -14.936 0.0
29.09995 135.146 -1.837 0.0
301.68771 123.672 -9.293 0.0
170.10893 124.022 -9.589 0.0
281.96526 63.544 -8.25 0.0
484.54485 149.565 -5.501 1.0
135.1571 92.749 -7.881 0.0
180.45342 137.899 -5.246 0.0
142.44526 85.406 -11.305 0.0
209.3971 93.233 -13.079 0.0
319.9473 122.936 -5.98 0.0
55.82322 249.325 -8.656 0.0
192.88771 124.006 -5.745 0.0
624.14322 128.988 -7.872 1.0
188.49914 107.264 -13.24 0.0
148.32281 150.075 -5.793 0.0
195.00363 49.31 -14.54 0.0
130.61179 100.208 -10.487 0.0
212.11383 111.048 -4.749 0.0
204.56444 92.076 -7.906 0.0
292.04853 135.932 -9.004 0.0
377.83465 73.336 -13.457 1.0
246.96118 116.761 -8.117 0.0
90.30485 39.3 -15.444 0.0
201.92608 123.558 -9.857 0.0
282.06975 136.09 -6.202 0.0
194.55955 119.488 -16.454 0.0
318.4322 140.467 -6.375 0.0
55.45751 121.476 -7.891 0.0
275.30404 90.024 -6.191 0.0
422.24281 131.994 -8.786 1.0
269.47873 88.921 -4.419 0.0
186.01751 55.271 -16.153 0.0
221.17832 94.967 -6.591 0.0
275.66975 94.999 -16.843 0.0
335.28118 90.129 -13.33 1.0
288.88771 102.96 -10.967 0.0
190.71955 88.269 -13.167 0.0
211.17342 126.741 -10.398 0.0
116.92363 140.09 -7.578 0.0
310.282 181.753 -17.61 0.0
184.21506 112.336 -8.764 0.0
248.21506 101.988 -6.487 0.0
116.00934 84.793 -9.057 0.0
299.88526 143.66 -7.279 0.0
1376.78322 107.066 -7.893 1.0
182.85669 191.559 -10.367 0.0
238.2624 48.592 -9.687 0.0
239.5424 105.47 -9.258 0.0
195.16036 127.911 -7.054 0.0
149.73342 118.643 -10.526 0.0
424.30649 62.8 -22.35 1.0
221.77914 104.983 -7.908 0.0
407.7971 126.983 -11.675 1.0
175.04608 120.542 -17.484 0.0
306.65098 120.0 -18.973 0.0
315.0624 85.82 -11.858 0.0
88.5024 211.429 -11.543 0.0
101.61587 19.215 -26.402 0.0
132.04853 186.123 -7.21 0.0
146.25914 200.16 -15.88 0.0
147.3824 104.658 -8.836 0.0
156.26404 135.353 -8.245 0.0
66.2722 115.129 -16.416 0.0
247.43138 124.991 -11.79 0.0
282.90567 115.472 -12.448 0.0
401.05751 125.015 -9.465 1.0
156.08118 88.128 -16.916 0.0
198.08608 133.961 -8.055 0.0
214.09914 84.353 -12.991 0.0
269.73995 161.953 -3.091 0.0
199.44444 169.922 -6.241 0.0
149.65506 190.802 -30.719 0.0
227.23873 120.14 -12.39 0.0

To generate a scatter plot matrix, click on the plot button bellow the table and select scatter. That will transform your table to a scatter plot matrix. It automatically picks all numeric columns as values. To include predicted clusters, click on Plot Options and drag prediction to the list of Keys. You will get the following plot. On the diagonal panels you see the PDF of marginal distribution of each variable. Non-diagonal panels show a scatter plot between variables of the two variables of the row and column. For example the top right panel shows the scatter plot between duration and loudness. Each point is colored according to the cluster it is assigned to.

display(transformed.sample(false, fraction = 0.01)) // try fraction=1.0 as this dataset is small
duration tempo loudness prediction
189.93587 134.957 -12.934 0.0
206.44526 135.26 -11.146 0.0
295.65342 137.904 -7.308 0.0
158.1971 174.831 -12.544 0.0
259.99628 171.094 -12.057 0.0
277.002 88.145 -6.039 0.0
1518.65424 65.003 -19.182 1.0
121.73016 85.041 -8.193 0.0
205.97506 106.952 -6.572 0.0
206.18404 89.447 -9.535 0.0
202.52689 134.13 -6.535 0.0
259.02975 97.948 -11.276 0.0
308.53179 80.017 -12.277 0.0
151.71873 117.179 -12.394 0.0
165.56363 99.187 -11.414 0.0
370.83383 67.495 -20.449 1.0
238.65424 100.071 -9.276 0.0
163.7873 119.924 -5.941 0.0
279.32689 67.371 -26.67 0.0
353.85424 68.405 -8.105 1.0
227.23873 117.62 -7.874 0.0
195.49995 85.916 -8.828 0.0
322.45506 135.826 -5.034 0.0
235.88526 109.773 -10.919 0.0
235.15383 163.924 -9.666 0.0
253.67465 125.014 -7.171 0.0
415.03302 71.991 -15.224 1.0
190.85016 152.805 -2.871 0.0
290.76853 84.841 -6.161 0.0
346.8273 129.981 -10.377 1.0
174.70649 143.446 -11.994 0.0
170.84036 70.033 -7.782 0.0
517.66812 151.948 -12.363 1.0
62.06649 154.406 -9.387 0.0
505.96526 90.59 -19.848 1.0
480.86159 0.0 -11.707 1.0
330.13506 204.534 -9.85 1.0
223.99955 110.3 -12.339 0.0
200.98567 89.215 -3.858 0.0
158.09261 178.826 -13.681 0.0
186.46159 110.102 -16.477 0.0
399.46404 125.03 -10.786 1.0
118.64771 85.747 -34.461 0.0
352.49587 91.139 -9.13 1.0
150.15138 106.364 -7.337 0.0
158.98077 124.54 -17.405 0.0
122.17424 170.018 -9.047 0.0
299.38893 91.976 -6.266 0.0
197.95546 142.744 -8.189 0.0
332.38159 89.071 -5.08 1.0
309.78567 136.05 -15.105 0.0
198.47791 82.546 -12.594 0.0
254.17098 144.01 -9.0 0.0
155.81995 233.022 -8.978 0.0
176.53506 136.255 -9.675 0.0
331.54567 221.511 -13.778 1.0
140.72118 162.44 -10.654 0.0
210.9122 120.039 -5.391 0.0
197.27628 119.396 -22.599 0.0
339.25179 96.842 -16.207 1.0
355.97016 142.777 -5.118 1.0
170.23955 55.107 -17.654 0.0
360.01914 119.997 -7.53 1.0
241.76281 101.938 -3.765 0.0
84.92363 236.863 -15.846 0.0
361.09016 120.121 -5.861 1.0
262.37342 89.924 -4.819 0.0
225.74975 139.994 -11.505 0.0
246.9873 172.147 -16.273 0.0
159.242 166.855 -4.771 0.0
192.86159 148.297 -13.423 0.0
140.90404 92.602 -12.604 0.0
224.20853 71.879 -16.615 0.0
235.78077 180.366 -3.918 0.0
244.45342 105.077 -5.004 0.0
210.57261 200.044 -11.381 0.0
327.3922 112.023 -11.341 1.0
168.38485 99.991 -4.1 0.0
287.13751 137.154 -12.948 0.0
148.63628 121.773 -11.432 0.0
214.7522 124.437 -5.834 0.0
197.43302 92.959 -4.948 0.0
150.17751 112.0 -5.968 0.0
152.86812 120.884 -15.693 0.0
173.322 120.827 -7.96 0.0
235.15383 85.519 -8.172 0.0
299.41506 94.68 -15.486 0.0
222.35383 156.046 -8.885 0.0
235.85914 130.055 -5.341 0.0
276.71465 170.059 -2.926 0.0
136.07138 168.895 -6.971 0.0
205.7922 129.57 -6.113 0.0
268.72118 126.894 -7.142 0.0
390.63465 232.08 -5.493 1.0
242.59873 124.034 -11.24 0.0
274.80771 108.178 -21.456 0.0
157.25669 151.108 -11.678 0.0
203.67628 140.02 -5.939 0.0
302.47138 148.2 -10.428 0.0
292.64934 106.006 -3.538 0.0
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displayHTML(frameIt("https://en.wikipedia.org/wiki/Euclidean_space",500)) // make sure you run the cell with first wikipedia article!

Do you see the problem in our clusters based on the plot?

As you can see there is very little "separation" (in the sense of being separable into two point clouds, that represent our two identifed clusters, such that they have minimal overlay of these two features, i.e. tempo and loudness. NOTE that this sense of "pairwise separation" is a 2D projection of all three features in 3D Euclidean Space, i.e. loudness, tempo and duration, that depends directly on their two-dimensional visually sense-making projection of perhaps two important song features, as depicted in the corresponding 2D-scatter-plot of tempo versus loudness within the 2D scatter plot matrix that is helping us to partially visualize in the 2D-plane all of the three features in the three dimensional real-valued feature space that was the input to our K-Means algorithm) between loudness, and tempo and generated clusters. To see that, focus on the panels in the first and second columns of the scatter plot matrix. For varying values of loudness and tempo prediction does not change. Instead, duration of a song alone predicts what cluster it belongs to. Why is that?

To see the reason, let's take a look at the marginal distribution of duration in the next cell.

To produce this plot, we have picked histogram from the plots menu and in Plot Options we chose prediction as key and duration as value. The histogram plot shows significant skew in duration. Basically there are a few very long songs. These data points have large leverage on the mean function (what KMeans uses for clustering).

display(transformed.sample(false, fraction = 1.0).select("duration", "prediction")) // plotting over all results
duration prediction
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There are known techniques for dealing with skewed features. A simple technique is applying a power transformation. We are going to use the simplest and most common power transformation: logarithm.

In following cell we repeat the clustering experiment with a transformed DataFrame that includes a new column called log_duration.

val df = table("songsTable").selectExpr("tempo", "loudness", "log(duration) as log_duration")
val trainingData2 = new VectorAssembler().
                  setInputCols(Array("log_duration", "tempo", "loudness")).
                  setOutputCol("features").
                  transform(df)
val model2 = new KMeans().setK(2).fit(trainingData2)
val transformed2 = model2.transform(trainingData2).select("log_duration", "tempo", "loudness", "prediction")
display(transformed2.sample(false, fraction = 0.1))
log_duration tempo loudness prediction
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5.291204127341661 104.378 -12.13 1.0
4.726046477037809 117.436 -26.354 1.0
4.914522552325214 156.8 -5.616 0.0
3.645320906144505 190.071 -8.348 0.0
6.217912752034596 127.986 -15.299 1.0
5.49699239016298 152.552 -9.21 0.0
4.91854054591316 171.014 -4.493 0.0
5.748533253386812 125.986 -9.382 1.0
5.686799476467082 105.387 -13.275 1.0
5.7666855967574575 60.453 -8.009 1.0
5.378686990009553 69.781 -10.723 1.0
5.305311003955202 100.036 -4.15 1.0
5.504991152805347 91.92 -4.939 1.0
5.271409371809784 202.926 -12.805 0.0
5.584003924284049 181.534 -15.531 0.0
6.215096858959298 130.013 -7.987 1.0
5.487092346805161 104.257 -9.098 1.0
5.754096429647435 238.327 -7.028 0.0
5.236179002727057 112.183 -14.136 1.0
5.452545386241633 89.064 -9.939 1.0
4.571933723436425 186.769 -11.649 0.0
5.74878302284854 126.157 -10.84 1.0
4.462453307085061 134.395 -4.727 0.0
5.229765094411506 143.875 -12.669 0.0
5.516293107703791 111.874 -10.131 1.0
4.986986110278029 92.72 -6.982 1.0
5.134594536181753 97.94 -14.83 1.0
5.94764368547729 120.983 -9.233 1.0
5.589973519371366 139.881 -11.774 0.0
5.832577543586846 108.428 -8.926 1.0
5.57404080623269 129.139 -4.393 1.0
5.737734073968367 138.816 -7.556 0.0
5.228365338789169 109.997 -10.253 1.0
5.478948537110532 84.271 -14.741 1.0
5.097132205437792 94.075 -3.565 1.0
5.7915577015049 111.001 -8.265 1.0
4.758836405626318 156.703 -9.588 0.0
5.268318568522543 70.923 -11.502 1.0
5.101912321360921 144.581 -10.228 0.0
5.607287873701992 94.022 -11.182 1.0
5.464231047351683 80.56 -5.019 1.0
5.82628048105143 144.995 -7.894 0.0
5.11862145971635 95.003 -6.393 1.0
5.226542700885508 144.35 -5.396 0.0
5.764803190566032 112.0 -9.303 1.0
4.7352630988107265 114.697 -4.575 1.0
5.316018719084458 141.976 -21.61 0.0
5.733516795474041 183.021 -11.119 0.0
5.305829678341554 86.122 -4.442 1.0
5.934733177365839 124.97 -18.222 1.0
5.253812766217677 96.969 -3.996 1.0
5.411294114932506 89.874 -6.8 1.0
4.551471791137433 80.11 -12.882 1.0
5.24654895931225 126.857 -11.178 1.0
5.52538935145276 88.999 -7.108 1.0
5.233395411909235 174.002 -4.727 0.0
5.062519840326649 172.201 -4.75 0.0
5.47709335356482 130.832 -19.444 1.0
6.546896021572621 175.921 -14.61 0.0
5.875580463550244 125.238 -8.638 1.0
5.547621681459602 182.05 -8.294 0.0
5.600552539550706 165.987 -5.869 0.0
5.330541303481353 100.578 -13.527 1.0
5.521426437267798 98.619 -8.239 1.0
5.0512127147107515 100.524 -13.862 1.0

The new clustering model makes much more sense. Songs with high tempo and loudness are put in one cluster and song duration does not affect song categories.

To really understand how the points in 3D behave you need to see them in 3D interactively and understand the limits of its three 2D projections. For this let us spend some time and play in sageMath Worksheet in CoCalc (it is free for light-weight use and perhaps worth the 7 USD a month if you need more serious computing in mathematics, statistics, etc. in multiple languages!).

Let us take a look at this sageMath Worksheet published here:

The point of the above little example is that you need to be able to tell a sensible story with your data science process and not just blindly apply a heuristic, but highly scalable, algorithm which depends on the notion of nearest neighborhoods defined by the metric (Euclidean distances in 3-dimensional real-valued spaces in this example) induced by the features you have engineered or have the power to re/re/...-engineer to increase the meaningfullness of the problem at hand.

Determining Optimal K

There are methods to find the optimal number of clusters. This partly depends on the purpose of the unsupervised learning task.

See here for some metrics in scala for the Irish dataset.

ScaDaMaLe Course site and book

Supervised Clustering with Decision Trees

Visual Introduction to decision trees and application to hand-written digit recognition

SOURCE: This is just a couple of decorations on a notebook published in databricks community edition in 2016.

Decision Trees for handwritten digit recognition

This notebook demonstrates learning a Decision Tree using Spark's distributed implementation. It gives the reader a better understanding of some critical hyperparameters for the tree learning algorithm, using examples to demonstrate how tuning the hyperparameters can improve accuracy.

Background: To learn more about Decision Trees, check out the resources at the end of this notebook. The visual description of ML and Decision Trees provides nice intuition helpful to understand this notebook, and Wikipedia gives lots of details.

Data: We use the classic MNIST handwritten digit recognition dataset. It is from LeCun et al. (1998) and may be found under "mnist" at the LibSVM dataset page.

Goal: Our goal for our data is to learn how to recognize digits (0 - 9) from images of handwriting. However, we will focus on understanding trees, not on this particular learning problem.

Takeaways: Decision Trees take several hyperparameters which can affect the accuracy of the learned model. There is no one "best" setting for these for all datasets. To get the optimal accuracy, we need to tune these hyperparameters based on our data.

Let's Build Intuition for Learning with Decision Trees

Load MNIST training and test datasets

Our datasets are vectors of pixels representing images of handwritten digits. For example:

Image of a digit Image of all 10 digits

These datasets are stored in the popular LibSVM dataset format. We will load them using MLlib's LibSVM dataset reader utility.

//-----------------------------------------------------------------------------------------------------------------
// using RDD-based MLlib - ok for Spark 1.x
// MLUtils.loadLibSVMFile returns an RDD.
//import org.apache.spark.mllib.util.MLUtils
//val trainingRDD = MLUtils.loadLibSVMFile(sc, "/databricks-datasets/mnist-digits/data-001/mnist-digits-train.txt")
//val testRDD = MLUtils.loadLibSVMFile(sc, "/databricks-datasets/mnist-digits/data-001/mnist-digits-test.txt")
// We convert the RDDs to DataFrames to use with ML Pipelines.
//val training = trainingRDD.toDF()
//val test = testRDD.toDF()
// Note: In Spark 1.6 and later versions, Spark SQL has a LibSVM data source.  The above lines can be simplified to:
//// val training = sqlContext.read.format("libsvm").load("/mnt/mllib/mnist-digits-csv/mnist-digits-train.txt")
//// val test = sqlContext.read.format("libsvm").load("/mnt/mllib/mnist-digits-csv/mnist-digits-test.txt")
//-----------------------------------------------------------------------------------------------------------------
val training = spark.read.format("libsvm")
                    .option("numFeatures", "780")
                    .load("/datasets/sds/mnist-digits/data-001/mnist-digits-train.txt")

val test = spark.read.format("libsvm")
                    .option("numFeatures", "780")
                    .load("/datasets/sds/mnist-digits/data-001/mnist-digits-test.txt")
// Cache data for multiple uses.
training.cache()
test.cache()

println(s"We have ${training.count} training images and ${test.count} test images.")
We have 60000 training images and 10000 test images.
training: org.apache.spark.sql.DataFrame = [label: double, features: vector]
test: org.apache.spark.sql.DataFrame = [label: double, features: vector]

Display our data. Each image has the true label (the label column) and a vector of features which represent pixel intensities (see below for details of what is in training).

training.printSchema()
root
 |-- label: double (nullable = true)
 |-- features: vector (nullable = true)
training.show(3) // replace 'true' by 'false' to see the whole row hidden by '...'
+-----+--------------------+
|label|            features|
+-----+--------------------+
|  5.0|(780,[152,153,154...|
|  0.0|(780,[127,128,129...|
|  4.0|(780,[160,161,162...|
+-----+--------------------+
only showing top 3 rows
display(training) // this is databricks-specific for interactive visual convenience

The pixel intensities are represented in features as a sparse vector, for example the first observation, as seen in row 1 of the output to display(training) or training.show(2,false) above, has label as 5, i.e. the hand-written image is for the number 5. And this hand-written image is the following sparse vector (just click the triangle to the left of the feature in first row to see the following):

type: 0
size: 780
indices: [152,153,155,...,682,683]
values: [3, 18, 18,18,126,...,132,16]

Here,

  • type: 0 says we have a sparse vector that only represents non-zero entries (as opposed to a dense vector where every entry is represented).
  • size: 780 says the vector has 780 indices in total
  • these indices from 0,...,779 are a unidimensional indexing of the two-dimensional array of pixels in the image
  • indices: [152,153,155,...,682,683] are the indices from the [0,1,...,779] possible indices with non-zero values
    • a value is an integer encoding the gray-level at the pixel index
  • values: [3, 18, 18,18,126,...,132,16] are the actual gray level values, for example:
    • at pixed index 152 the gray-level value is 3,
    • at index 153 the gray-level value is 18,
    • ..., and finally at
    • at index 683 the gray-level value is 18

Train a Decision Tree

We begin by training a decision tree using the default settings. Before training, we want to tell the algorithm that the labels are categories 0-9, rather than continuous values. We use the StringIndexer class to do this. We tie this feature preprocessing together with the tree algorithm using a Pipeline. ML Pipelines are tools Spark provides for piecing together Machine Learning algorithms into workflows. To learn more about Pipelines, check out other ML example notebooks in Databricks and the ML Pipelines user guide. Also See mllib-decision-tree.html#basic-algorithm.

// Import the ML algorithms we will use.
import org.apache.spark.ml.classification.{DecisionTreeClassifier, DecisionTreeClassificationModel}
import org.apache.spark.ml.feature.StringIndexer
import org.apache.spark.ml.Pipeline
import org.apache.spark.ml.classification.{DecisionTreeClassifier, DecisionTreeClassificationModel}
import org.apache.spark.ml.feature.StringIndexer
import org.apache.spark.ml.Pipeline
// StringIndexer: Read input column "label" (digits) and annotate them as categorical values.
val indexer = new StringIndexer().setInputCol("label").setOutputCol("indexedLabel")

// DecisionTreeClassifier: Learn to predict column "indexedLabel" using the "features" column.
val dtc = new DecisionTreeClassifier().setLabelCol("indexedLabel")

// Chain indexer + dtc together into a single ML Pipeline.
val pipeline = new Pipeline().setStages(Array(indexer, dtc))
indexer: org.apache.spark.ml.feature.StringIndexer = strIdx_cdb9fb742f94
dtc: org.apache.spark.ml.classification.DecisionTreeClassifier = dtc_9345fcaec0f5
pipeline: org.apache.spark.ml.Pipeline = pipeline_a426bd538000

Now, let's fit a model to our data.

val model = pipeline.fit(training)
model: org.apache.spark.ml.PipelineModel = pipeline_a426bd538000

We can inspect the learned tree by displaying it using Databricks ML visualization. (Visualization is available for several but not all models.)

// The tree is the last stage of the Pipeline.  Display it!
val tree = model.stages.last.asInstanceOf[DecisionTreeClassificationModel]
display(tree)
treeNode
{"index":31,"featureType":"continuous","prediction":null,"threshold":133.5,"categories":null,"feature":350,"overflow":false}
{"index":15,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":568,"overflow":false}
{"index":7,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":430,"overflow":false}
{"index":3,"featureType":"continuous","prediction":null,"threshold":2.5,"categories":null,"feature":405,"overflow":false}
{"index":1,"featureType":"continuous","prediction":null,"threshold":12.5,"categories":null,"feature":485,"overflow":false}
{"index":0,"featureType":null,"prediction":1.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":2,"featureType":null,"prediction":4.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":5,"featureType":"continuous","prediction":null,"threshold":14.5,"categories":null,"feature":516,"overflow":false}
{"index":4,"featureType":null,"prediction":9.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":6,"featureType":null,"prediction":7.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":11,"featureType":"continuous","prediction":null,"threshold":34.5,"categories":null,"feature":211,"overflow":false}
{"index":9,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":98,"overflow":false}
{"index":8,"featureType":null,"prediction":8.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":10,"featureType":null,"prediction":6.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":13,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":156,"overflow":false}
{"index":12,"featureType":null,"prediction":4.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":14,"featureType":null,"prediction":6.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":23,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":435,"overflow":false}
{"index":19,"featureType":"continuous","prediction":null,"threshold":10.5,"categories":null,"feature":489,"overflow":false}
{"index":17,"featureType":"continuous","prediction":null,"threshold":2.5,"categories":null,"feature":380,"overflow":false}
{"index":16,"featureType":null,"prediction":5.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":18,"featureType":null,"prediction":9.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":21,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":320,"overflow":false}
{"index":20,"featureType":null,"prediction":3.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":22,"featureType":null,"prediction":9.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":27,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":346,"overflow":false}
{"index":25,"featureType":"continuous","prediction":null,"threshold":97.5,"categories":null,"feature":348,"overflow":false}
{"index":24,"featureType":null,"prediction":3.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":26,"featureType":null,"prediction":7.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":29,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":655,"overflow":false}
{"index":28,"featureType":null,"prediction":6.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":30,"featureType":null,"prediction":7.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":47,"featureType":"continuous","prediction":null,"threshold":36.5,"categories":null,"feature":489,"overflow":false}
{"index":39,"featureType":"continuous","prediction":null,"threshold":26.5,"categories":null,"feature":290,"overflow":false}
{"index":35,"featureType":"continuous","prediction":null,"threshold":100.5,"categories":null,"feature":486,"overflow":false}
{"index":33,"featureType":"continuous","prediction":null,"threshold":129.5,"categories":null,"feature":490,"overflow":false}
{"index":32,"featureType":null,"prediction":2.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":34,"featureType":null,"prediction":0.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":37,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":656,"overflow":false}
{"index":36,"featureType":null,"prediction":3.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":38,"featureType":null,"prediction":7.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":43,"featureType":"continuous","prediction":null,"threshold":5.5,"categories":null,"feature":297,"overflow":false}
{"index":41,"featureType":"continuous","prediction":null,"threshold":169.5,"categories":null,"feature":486,"overflow":false}
{"index":40,"featureType":null,"prediction":9.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":42,"featureType":null,"prediction":6.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":45,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":598,"overflow":false}
{"index":44,"featureType":null,"prediction":4.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":46,"featureType":null,"prediction":7.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":55,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":521,"overflow":false}
{"index":51,"featureType":"continuous","prediction":null,"threshold":7.5,"categories":null,"feature":347,"overflow":false}
{"index":49,"featureType":"continuous","prediction":null,"threshold":4.5,"categories":null,"feature":206,"overflow":false}
{"index":48,"featureType":null,"prediction":0.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":50,"featureType":null,"prediction":3.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":53,"featureType":"continuous","prediction":null,"threshold":16.5,"categories":null,"feature":514,"overflow":false}
{"index":52,"featureType":null,"prediction":4.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":54,"featureType":null,"prediction":7.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":59,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":658,"overflow":false}
{"index":57,"featureType":"continuous","prediction":null,"threshold":8.5,"categories":null,"feature":555,"overflow":false}
{"index":56,"featureType":null,"prediction":6.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":58,"featureType":null,"prediction":3.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":61,"featureType":"continuous","prediction":null,"threshold":12.5,"categories":null,"feature":543,"overflow":false}
{"index":60,"featureType":null,"prediction":0.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":62,"featureType":null,"prediction":7.0,"threshold":null,"categories":null,"feature":null,"overflow":false}

Above, we can see how the tree makes predictions. When classifying a new example, the tree starts at the "root" node (at the top). Each tree node tests a pixel value and goes either left or right. At the bottom "leaf" nodes, the tree predicts a digit as the image's label.

Hyperparameter Tuning

Run the next cell and come back into hyper-parameter tuning for a couple minutes.

Exploring "maxDepth": training trees of different sizes

In this section, we test tuning a single hyperparameter maxDepth, which determines how deep (and large) the tree can be. We will train trees at varying depths and see how it affects the accuracy on our held-out test set.

Note: The next cell can take about 1 minute to run since it is training several trees which get deeper and deeper.

val variedMaxDepthModels = (0 until 8).map { maxDepth =>
  // For this setting of maxDepth, learn a decision tree.
  dtc.setMaxDepth(maxDepth)
  // Create a Pipeline with our feature processing stage (indexer) plus the tree algorithm
  val pipeline = new Pipeline().setStages(Array(indexer, dtc))
  // Run the ML Pipeline to learn a tree.
  pipeline.fit(training)
}
variedMaxDepthModels: scala.collection.immutable.IndexedSeq[org.apache.spark.ml.PipelineModel] = Vector(pipeline_e96074b3bded, pipeline_12646faf8260, pipeline_d5f639d6a180, pipeline_4034c9138161, pipeline_83215a1ed684, pipeline_8737125f5dcc, pipeline_02a6caa4d542, pipeline_88827be266ae)

We will use the default metric to evaluate the performance of our classifier:

// Define an evaluation metric.  In this case, we will use "accuracy".
import org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator
val evaluator = new MulticlassClassificationEvaluator().setLabelCol("indexedLabel").setMetricName("f1") // default MetricName
import org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator
evaluator: org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator = MulticlassClassificationEvaluator: uid=mcEval_0ee0afcb7621, metricName=f1, metricLabel=0.0, beta=1.0, eps=1.0E-15
// For each maxDepth setting, make predictions on the test data, and compute the classifier's f1 performance metric.
val f1MetricPerformanceMeasures = (0 until 8).map { maxDepth =>
  val model = variedMaxDepthModels(maxDepth)
  // Calling transform() on the test set runs the fitted pipeline.
  // The learned model makes predictions on each test example.
  val predictions = model.transform(test)
  // Calling evaluate() on the predictions DataFrame computes our performance metric.
  (maxDepth, evaluator.evaluate(predictions))
}.toDF("maxDepth", "f1")
f1MetricPerformanceMeasures: org.apache.spark.sql.DataFrame = [maxDepth: int, f1: double]

We can display our accuracy results and see immediately that deeper, larger trees are more powerful classifiers, achieving higher accuracies.

Note: When you run f1MetricPerformanceMeasures.show(), you will get a table with f1 score getting better (i.e., approaching 1) with depth.

f1MetricPerformanceMeasures.show()
+--------+-------------------+
|maxDepth|                 f1|
+--------+-------------------+
|       0|  0.023138302649304|
|       1|0.07692344325297736|
|       2|0.21454218035530098|
|       3|0.43262516590643385|
|       4| 0.5918539983626627|
|       5| 0.6806954435278861|
|       6| 0.7478698562916142|
|       7| 0.7876393954574569|
+--------+-------------------+

Even though deeper trees are more powerful, they are not always better (recall from the SF/NYC city classification from house features at The visual description of ML and Decision Trees). If we kept increasing the depth on a rich enough dataset, training would take longer and longer. We also might risk overfitting (fitting the training data so well that our predictions get worse on test data); it is important to tune parameters based on held-out data to prevent overfitting. This will ensure that the fitted model generalizes well to yet unseen data, i.e. minimizes generalization error in a mathematical statistical sense.

Exploring "maxBins": discretization for efficient distributed computing

This section explores a more expert-level setting maxBins. For efficient distributed training of Decision Trees, Spark and most other libraries discretize (or "bin") continuous features (such as pixel values) into a finite number of values. This is an important step for the distributed implementation, but it introduces a tradeoff: Larger maxBins mean your data will be more accurately represented, but it will also mean more communication (and slower training).

The default value of maxBins generally works, but it is interesting to explore on our handwritten digit dataset. Remember our digit image from above:

Image of a digit

It is grayscale. But if we set maxBins = 2, then we are effectively making it a black-and-white image, not grayscale. Will that affect the accuracy of our model? Let's see!

Note: The next cell can take about 35 seconds to run since it trains several trees. Read the details on maxBins at mllib-decision-tree.html#split-candidates.

dtc.setMaxDepth(6) // Set maxDepth to a reasonable value.
// now try the maxBins "hyper-parameter" which actually acts as a "coarsener" 
//     mathematical researchers should note that it is a sub-algebra of the finite 
//     algebra of observable pixel images at the finest resolution available to us
// giving a compression of the image to fewer coarsely represented pixels
val f1MetricPerformanceMeasures = Seq(2, 4, 8, 16, 32).map { case maxBins =>
  // For this value of maxBins, learn a tree.
  dtc.setMaxBins(maxBins)
  val pipeline = new Pipeline().setStages(Array(indexer, dtc))
  val model = pipeline.fit(training)
  // Make predictions on test data, and compute accuracy.
  val predictions = model.transform(test)
  (maxBins, evaluator.evaluate(predictions))
}.toDF("maxBins", "f1")
f1MetricPerformanceMeasures: org.apache.spark.sql.DataFrame = [maxBins: int, f1: double]
f1MetricPerformanceMeasures.show()
+-------+------------------+
|maxBins|                f1|
+-------+------------------+
|      2|0.7429289482693366|
|      4|0.7390759023032782|
|      8|0.7443669963407805|
|     16|0.7426765688669141|
|     32|0.7478698562916142|
+-------+------------------+

We can see that extreme discretization (black and white) hurts performance as measured by F1-error, but only a bit. Using more bins increases the accuracy (but also makes learning more costly).

What's next?

  • Explore: Try out tuning other parameters of trees---or even ensembles like Random Forests or Gradient-Boosted Trees.
  • Automated tuning: This type of tuning does not have to be done by hand. (We did it by hand here to show the effects of tuning in detail.) MLlib provides automated tuning functionality via CrossValidator. Check out the other Databricks ML Pipeline guides or the Spark ML user guide for details.

Resources

If you are interested in learning more on these topics, these resources can get you started:

ScaDaMaLe Course site and book

Linear Algebra Review

This is a breeze'y scalarific break-down of:

Using the above resources we'll provide a review of basic linear algebra concepts that will recur throughout the course. These concepts include:

  • Matrices
  • Vectors
  • Arithmetic operations with vectors and matrices

We will see the accompanying Scala computations in the local or non-distributed setting.

Let's get a quick visual geometric interpretation for vectors, matrices and matrix-vector multiplications, eigen systems with real and comples Eigen values NOW from the following interactive visual-cognitive aid at:

Breeze is a linear algebra package in Scala. First, let us import it as follows:

import breeze.linalg._
import breeze.linalg._

1. Matrix: creation and element-access

A matrix is a two-dimensional array.

Let us denote matrices via bold uppercase letters as follows:

For instance, the matrix below is denoted with \(\mathbf{A}\), a capital bold A.

\[ \mathbf{A} = \begin{pmatrix} a_{11} & a_{12} & a_{13} \ a_{21} & a_{22} & a_{23} \ a_{31} & a_{32} & a_{33} \end{pmatrix} \]

We usually put commas between the row and column indexing sub-scripts, to make the possibly multi-digit indices distinguishable as follows:

\[ \mathbf{A} = \begin{pmatrix} a_{1,1} & a_{1,2} & a_{1,3} \ a_{2,1} & a_{2,2} & a_{2,3} \ a_{3,1} & a_{3,2} & a_{3,3} \end{pmatrix} \]

  • \(\mathbf{A}_{i,j}\) denotes the entry in \(i\)-th row and \(j\)-th column of the matrix \(\mathbf{A}\).
  • So for instance,
    • the first entry, the top left entry, is denoted by \(\mathbf{A}_{1,1}\).
    • And the entry in the third row and second column is denoted by \(\mathbf{A}_{3,2}\).
    • We say that a matrix with n rows and m columns is an \(n\) by \(m\) matrix and written as \(n \times m\)
      • The matrix \(\mathbf{A}\) shown above is a generic \(3 \times 3\) (pronounced 3-by-3) matrix.
      • And the matrix in Ameet's example in the video above, having 4 rows and 3 columns, is a 4 by 3 matrix.
    • If a matrix \(\mathbf{A}\) is \(n \times m\), we write:
      • \(\mathbf{A} \in \mathbb{R}^{n \times m}\) and say that \(\mathbf{A}\) is an \(\mathbb{R}\) to the power of the n times m,
        • where, \(\mathbb{R}\) here denotes the set of all real numbers in the line given by the open interval: \((-\infty,+\infty)\).

Let us created a matrix A as a val (that is immutable) in scala. The matrix we want to create is mathematically notated as follows:

\[ \mathbf{A} = \begin{pmatrix} a_{1,1} & a_{1,2} & a_{1,3} \ a_{2,1} & a_{2,2} & a_{2,3} \end{pmatrix}

\begin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \end{pmatrix} \]

val A = DenseMatrix((1, 2, 3), (4, 5, 6)) // let's create this 2 by 3 matrix
A: breeze.linalg.DenseMatrix[Int] =
1  2  3
4  5  6
A.size
res0: Int = 6
A.rows // number of rows
res1: Int = 2
A.size / A.rows // num of columns
res2: Int = 3
A.cols // also say
res3: Int = 3

Now, let's access the element \(a_{1,1}\), i.e., the element from the first row and first column of \(\mathbf{A}\), which in our val A matrix is the integer of type Int equalling 1.

A(0, 0) // Remember elements are indexed by zero in scala
res4: Int = 1

Gotcha: indices in breeze matrices start at 0 as in numpy of python and not at 1 as in MATLAB!

Of course if you assign the same dense matrix to a mutable var B then its entries can be modified as follows:

var B = DenseMatrix((1, 2, 3), (4, 5, 6))
B: breeze.linalg.DenseMatrix[Int] =
1  2  3
4  5  6
B(0,0)=999; B(1,1)=969; B(0,2)=666
B
res5: breeze.linalg.DenseMatrix[Int] =
999  2    666
4    969  6
  • A vector is a matrix with many rows and one column.

  • We'll denote a vector by bold lowercase letters: \[\mathbf{a} = \begin{pmatrix} 3.3 \ 1.0 \ 6.3 \ 3.6 \end{pmatrix}\]

    So, the vector above is denoted by \(\mathbf{a}\), the lowercase, bold a.

  • \(a_i\) denotes the i-th entry of a vector. So for instance:

    • \(a_2\) denotes the second entry of the vector and it is 1.0 for our vector.
  • If a vector is m-dimensional, then we say that \(\mathbf{a}\) is in \(\mathbb{R}^m\) and write \(\mathbf{a} \in \ \mathbb{R}^m\).

    • So our \(\mathbf{a} \in \ \mathbb{R}^4\).
val a = DenseVector(3.3, 1.0, 6.3, 3.6) // these are row vectors
a: breeze.linalg.DenseVector[Double] = DenseVector(3.3, 1.0, 6.3, 3.6)
a.size // a is a column vector of size 4
res6: Int = 4
a(1) // the second element of a is indexed by 1 as the first element is indexed by 0
res7: Double = 1.0
val a = DenseVector[Double](5, 4, -1) // this makes a vector of Doubles from input Int
a: breeze.linalg.DenseVector[Double] = DenseVector(5.0, 4.0, -1.0)
val a = DenseVector(5.0, 4.0, -1.0) // this makes a vector of Doubles from type inference . NOTE "5.0" is needed not just "5."
a: breeze.linalg.DenseVector[Double] = DenseVector(5.0, 4.0, -1.0)
val x = DenseVector.zeros[Double](5) // this will output x: breeze.linalg.DenseVector[Double] = DenseVector(0.0, 0.0, 0.0, 0.0, 0.0)
x: breeze.linalg.DenseVector[Double] = DenseVector(0.0, 0.0, 0.0, 0.0, 0.0)
val A = DenseMatrix((1, 4), (6, 1), (3, 5)) // let's create this 2 by 3 matrix
A: breeze.linalg.DenseMatrix[Int] =
1  4
6  1
3  5
A.t // transpose of A
res8: breeze.linalg.DenseMatrix[Int] =
1  6  3
4  1  5
val a = DenseVector(3.0, 4.0, 1.0)
a: breeze.linalg.DenseVector[Double] = DenseVector(3.0, 4.0, 1.0)
a.t
res9: breeze.linalg.Transpose[breeze.linalg.DenseVector[Double]] = Transpose(DenseVector(3.0, 4.0, 1.0))
val A = DenseMatrix((1, 4), (6, 1), (3, 5)) 
A: breeze.linalg.DenseMatrix[Int] =
1  4
6  1
3  5
val B = -A 
B: breeze.linalg.DenseMatrix[Int] =
-1  -4
-6  -1
-3  -5
A + B // should be A-A=0
res10: breeze.linalg.DenseMatrix[Int] =
0  0
0  0
0  0
A - B // should be A+A=2A
res11: breeze.linalg.DenseMatrix[Int] =
2   8
12  2
6   10
B - A // should be -A-A=-2A
res12: breeze.linalg.DenseMatrix[Int] =
-2   -8
-12  -2
-6   -10

Operators

All Tensors support a set of operators, similar to those used in Matlab or Numpy.

For HOMEWORK see: Workspace -> scalable-data-science -> xtraResources -> LinearAlgebra -> LAlgCheatSheet for a list of most of the operators and various operations.

Some of the basic ones are reproduced here, to give you an idea.

OperationBreezeMatlabNumpy
Elementwise additiona + ba + ba + b
Elementwise multiplicationa :* ba .* ba * b
Elementwise comparisona :< ba < b (gives matrix of 1/0 instead of true/false)a < b
Inplace additiona :+= 1.0a += 1a += 1
Inplace elementwise multiplicationa :*= 2.0a *= 2a *= 2
Vector dot producta dot b,a.t * bdot(a,b)dot(a,b)
Elementwise sumsum(a)sum(sum(a))a.sum()
Elementwise maxa.maxmax(a)a.max()
Elementwise argmaxargmax(a)argmax(a)a.argmax()
Ceilingceil(a)ceil(a)ceil(a)
Floorfloor(a)floor(a)floor(a)

Pop Quiz:

  • what is a natural geometric interpretation of scalar multiplication of a vector or a matrix and what about vector matrix multiplication?

Let's get a quick visual geometric interpretation for vectors, matrices and matrix-vector multiplications from the first interactive visual-cognitive aid at:

val A = DenseMatrix((1, 4), (6, 1), (3, 5)) 
A: breeze.linalg.DenseMatrix[Int] =
1  4
6  1
3  5
5 * A
res13: breeze.linalg.DenseMatrix[Int] =
5   20
30  5
15  25
A * 5
res14: breeze.linalg.DenseMatrix[Int] =
5   20
30  5
15  25
val A = DenseMatrix((1, 4), (6, 1), (3, 5)) 
A: breeze.linalg.DenseMatrix[Int] =
1  4
6  1
3  5
val B = DenseMatrix((3, 1), (2, 2), (1, 3)) 
B: breeze.linalg.DenseMatrix[Int] =
3  1
2  2
1  3
A *:* B // element-wise multiplication
res15: breeze.linalg.DenseMatrix[Int] =
3   4
12  2
3   15
val A = DenseMatrix((1, 4), (3, 1)) 
A: breeze.linalg.DenseMatrix[Int] =
1  4
3  1
val a = DenseVector(1, -1) // is a column vector
a: breeze.linalg.DenseVector[Int] = DenseVector(1, -1)
a.size // a is a column vector of size 2
res16: Int = 2
A * a
res17: breeze.linalg.DenseVector[Int] = DenseVector(-3, 2)
val A = DenseMatrix((1,2,3),(1,1,1))
A: breeze.linalg.DenseMatrix[Int] =
1  2  3
1  1  1
val B = DenseMatrix((4, 1), (9, 2), (8, 9))
B: breeze.linalg.DenseMatrix[Int] =
4  1
9  2
8  9
A*B // 4+18+14
res18: breeze.linalg.DenseMatrix[Int] =
46  32
21  12
1*4 + 2*9 + 3*8 // checking first entry of A*B
res19: Int = 46
val A = DenseMatrix((1,2,3),(4,5,6))
A: breeze.linalg.DenseMatrix[Int] =
1  2  3
4  5  6
DenseMatrix.eye[Int](3)
res20: breeze.linalg.DenseMatrix[Int] =
1  0  0
0  1  0
0  0  1
A * DenseMatrix.eye[Int](3)
res21: breeze.linalg.DenseMatrix[Int] =
1  2  3
4  5  6
DenseMatrix.eye[Int](2) * A
res22: breeze.linalg.DenseMatrix[Int] =
1  2  3
4  5  6
val D = DenseMatrix((2.0, 3.0), (4.0, 5.0))
val Dinv = inv(D)
D: breeze.linalg.DenseMatrix[Double] =
2.0  3.0
4.0  5.0
Dinv: breeze.linalg.DenseMatrix[Double] =
-2.5  1.5
2.0   -1.0
D * Dinv
res23: breeze.linalg.DenseMatrix[Double] =
1.0  0.0
0.0  1.0
Dinv * D
res24: breeze.linalg.DenseMatrix[Double] =
1.0  0.0
0.0  1.0
val b = DenseVector(4, 3)
norm(b)
b: breeze.linalg.DenseVector[Int] = DenseVector(4, 3)
res25: Double = 5.0
Math.sqrt(4*4 + 3*3) // check
res26: Double = 5.0

HOMEWORK: read this! https://github.com/scalanlp/breeze/wiki/Quickstart

It is here in markdown'd via wget and pandoc for your convenience.

Scala / nlp / breeze / Quickstart

David Hall edited this page on 24 Dec 2015

Breeze is modeled on Scala, and so if you're familiar with it, you'll be familiar with Breeze. First, import the linear algebra package:

scala> import breeze.linalg._

Let's create a vector:

scala> val x = DenseVector.zeros[Double](5)
x: breeze.linalg.DenseVector[Double] = DenseVector(0.0, 0.0, 0.0, 0.0, 0.0)

Here we make a column vector of zeros of type Double. And there are other ways we could create the vector - such as with a literal DenseVector(1,2,3) or with a call to fill or tabulate. The vector is "dense" because it is backed by an Array[Double], but could as well have created a SparseVector.zeros[Double](5), which would not allocate memory for zeros.

Unlike Scalala, all Vectors are column vectors. Row vectors are represented as Transpose[Vector[T]].

The vector object supports accessing and updating data elements by their index in 0 to x.length-1. Like Numpy, negative indices are supported, with the semantics that for an index i < 0 we operate on the i-th element from the end (x(i) == x(x.length + i)).

scala> x(0)
Double = 0.0

scala> x(1) = 2

scala> x
breeze.linalg.DenseVector[Double] = DenseVector(0.0, 2.0, 0.0, 0.0, 0.0)

Breeze also supports slicing. Note that slices using a Range are much, much faster than those with an arbitrary sequence.

scala> x(3 to 4) := .5
breeze.linalg.DenseVector[Double] = DenseVector(0.5, 0.5)

scala> x
breeze.linalg.DenseVector[Double] = DenseVector(0.0, 2.0, 0.0, 0.5, 0.5)

The slice operator constructs a read-through and write-through view of the given elements in the underlying vector. You set its values using the vectorized-set operator :=. You could as well have set it to a compatibly sized Vector.

scala> x(0 to 1) := DenseVector(.1,.2)

scala> x
breeze.linalg.DenseVector[Double] = DenseVector(0.1, 0.2, 0.0, 0.5, 0.5)

Similarly, a DenseMatrix can be created with a constructor method call, and its elements can be accessed and updated.

scala> val m = DenseMatrix.zeros[Int](5,5)
m: breeze.linalg.DenseMatrix[Int] = 
0  0  0  0  0  
0  0  0  0  0  
0  0  0  0  0  
0  0  0  0  0  
0  0  0  0  0  

The columns of m can be accessed as DenseVectors, and the rows as DenseMatrices.

scala> (m.rows, m.cols)
(Int, Int) = (5,5)

scala> m(::,1)
breeze.linalg.DenseVector[Int] = DenseVector(0, 0, 0, 0, 0)

scala>  m(4,::) := DenseVector(1,2,3,4,5).t  // transpose to match row shape
breeze.linalg.DenseMatrix[Int] = 1  2  3  4  5 

scala> m
breeze.linalg.DenseMatrix[Int] = 
0  0  0  0  0  
0  0  0  0  0  
0  0  0  0  0  
0  0  0  0  0  
1  2  3  4  5   

Assignments with incompatible cardinality or a larger numeric type won't compile.

scala> m := x
<console>:13: error: could not find implicit value for parameter op: breeze.linalg.operators.BinaryUpdateOp[breeze.linalg.DenseMatrix[Int],breeze.linalg.DenseVector[Double],breeze.linalg.operators.OpSet]
              m := x
                ^

Assignments with incompatible size will throw an exception:

scala> m := DenseMatrix.zeros[Int](3,3)
java.lang.IllegalArgumentException: requirement failed: Matrices must have same number of row

Sub-matrices can be sliced and updated, and literal matrices can be specified using a simple tuple-based syntax. Unlike Scalala, only range slices are supported, and only the columns (or rows for a transposed matrix) can have a Range step size different from 1.

scala> m(0 to 1, 0 to 1) := DenseMatrix((3,1),(-1,-2)) 
breeze.linalg.DenseMatrix[Int] = 
3   1   
-1  -2  

scala> m
breeze.linalg.DenseMatrix[Int] = 
3   1   0  0  0  
-1  -2  0  0  0  
0   0   0  0  0  
0   0   0  0  0  
1   2   3  4  5  

Broadcasting

Sometimes we want to apply an operation to every row or column of a matrix, as a unit. For instance, you might want to compute the mean of each row, or add a vector to every column. Adapting a matrix so that operations can be applied column-wise or row-wise is called broadcasting. Languages like R and numpy automatically and implicitly do broadcasting, meaning they won't stop you if you accidentally add a matrix and a vector. In Breeze, you have to signal your intent using the broadcasting operator *. The * is meant to evoke "foreach" visually. Here are some examples:

scala> import breeze.stats.mean

scala> val dm = DenseMatrix((1.0,2.0,3.0),
                            (4.0,5.0,6.0))

scala> val res = dm(::, *) + DenseVector(3.0, 4.0)
breeze.linalg.DenseMatrix[Double] =
4.0  5.0  6.0
8.0  9.0  10.0

scala> res(::, *) := DenseVector(3.0, 4.0)

scala> res
breeze.linalg.DenseMatrix[Double] =
3.0  3.0  3.0
4.0  4.0  4.0

scala> mean(dm(*, ::))
breeze.linalg.DenseVector[Double] = DenseVector(2.0, 5.0)

breeze.stats.distributions

Breeze also provides a fairly large number of probability distributions. These come with access to probability density function for either discrete or continuous distributions. Many distributions also have methods for giving the mean and the variance.

scala> import breeze.stats.distributions._

scala> val poi = new Poisson(3.0);
poi: breeze.stats.distributions.Poisson = <function1>

scala> val s = poi.sample(5);
s: IndexedSeq[Int] = Vector(5, 4, 5, 7, 4)

scala> s map { poi.probabilityOf(_) }
IndexedSeq[Double] = Vector(0.10081881344492458, 0.16803135574154085, 0.10081881344492458, 0.02160403145248382, 0.16803135574154085)

scala> val doublePoi = for(x <- poi) yield x.toDouble // meanAndVariance requires doubles, but Poisson samples over Ints
doublePoi: breeze.stats.distributions.Rand[Double] = breeze.stats.distributions.Rand$$anon$11@1b52e04

scala> breeze.stats.meanAndVariance(doublePoi.samples.take(1000));
breeze.stats.MeanAndVariance = MeanAndVariance(2.9960000000000067,2.9669509509509533,1000)

scala> (poi.mean,poi.variance)
(Double, Double) = (3.0,3.0)

NOTE: Below, there is a possibility of confusion for the term rate in the family of exponential distributions. Breeze parameterizes the distribution with the mean, but refers to it as the rate.

scala> val expo = new Exponential(0.5);
expo: breeze.stats.distributions.Exponential = Exponential(0.5)

scala> expo.rate
Double = 0.5

A characteristic of exponential distributions is its half-life, but we can compute the probability a value falls between any two numbers.

scala> expo.probability(0, log(2) * expo.rate)
Double = 0.5

scala> expo.probability(0.0, 1.5)
Double = 0.950212931632136

This means that approximately 95% of the draws from an exponential distribution fall between 0 and thrice the mean. We could have easily computed this with the cumulative distribution as well

scala> 1 - exp(-3.0)
Double = 0.950212931632136


scala> val samples = expo.sample(2).sorted;
samples: IndexedSeq[Double] = Vector(1.1891135726280517, 2.325607782657507)

scala> expo.probability(samples(0), samples(1));
Double = 0.08316481553047272

scala> breeze.stats.meanAndVariance(expo.samples.take(10000));
breeze.stats.MeanAndVariance = MeanAndVariance(2.029351863973081,4.163267835527843,10000)

scala> (1 / expo.rate, 1 / (expo.rate * expo.rate))
(Double, Double) = (2.0,4.0)

breeze.optimize

TODO: document breeze.optimize.minimize, recommend that instead.

Breeze's optimization package includes several convex optimization routines and a simple linear program solver. Convex optimization routines typically take a DiffFunction[T], which is a Function1 extended to have a gradientAt method, which returns the gradient at a particular point. Most routines will require a breeze.linalg-enabled type: something like a Vector or a Counter.

Here's a simple DiffFunction: a parabola along each vector's coordinate.

scala> import breeze.optimize._

scala>  val f = new DiffFunction[DenseVector[Double]] {
     |               def calculate(x: DenseVector[Double]) = {
     |                 (norm((x - 3d) :^ 2d,1d),(x * 2d) - 6d);
     |               }
     |             }
f: java.lang.Object with breeze.optimize.DiffFunction[breeze.linalg.DenseVector[Double]] = $anon$1@617746b2

Note that this function takes its minimum when all values are 3. (It's just a parabola along each coordinate.)

scala> f.valueAt(DenseVector(3,3,3))
Double = 0.0

scala> f.gradientAt(DenseVector(3,0,1))
breeze.linalg.DenseVector[Double] = DenseVector(0.0, -6.0, -4.0)

scala>  f.calculate(DenseVector(0,0))
(Double, breeze.linalg.DenseVector[Double]) = (18.0,DenseVector(-6.0, -6.0))

You can also use approximate derivatives, if your function is easy enough to compute:

scala> def g(x: DenseVector[Double]) = (x - 3.0):^ 2.0 sum

scala> g(DenseVector(0.,0.,0.))
Double = 27.0

scala> val diffg = new ApproximateGradientFunction(g)

scala> diffg.gradientAt(DenseVector(3,0,1))
breeze.linalg.DenseVector[Double] = DenseVector(1.000000082740371E-5, -5.999990000127297, -3.999990000025377)

Ok, now let's optimize f. The easiest routine to use is just LBFGS, which is a quasi-Newton method that works well for most problems.

scala> val lbfgs = new LBFGS[DenseVector[Double]](maxIter=100, m=3) // m is the memory. anywhere between 3 and 7 is fine. The larger m, the more memory is needed.

scala> val optimum = lbfgs.minimize(f,DenseVector(0,0,0))
optimum: breeze.linalg.DenseVector[Double] = DenseVector(2.9999999999999973, 2.9999999999999973, 2.9999999999999973)

scala> f(optimum)
Double = 2.129924444096732E-29

That's pretty close to 0! You can also use a configurable optimizer, using FirstOrderMinimizer.OptParams. It takes several parameters:

case class OptParams(batchSize:Int = 512,
                     regularization: Double = 1.0,
                     alpha: Double = 0.5,
                     maxIterations:Int = -1,
                     useL1: Boolean = false,
                     tolerance:Double = 1E-4,
                     useStochastic: Boolean= false) {
  // ...
}

batchSize applies to BatchDiffFunctions, which support using small minibatches of a dataset. regularization integrates L2 or L1 (depending on useL1) regularization with constant lambda. alpha controls the initial stepsize for algorithms that need it. maxIterations is the maximum number of gradient steps to be taken (or -1 for until convergence). tolerance controls the sensitivity of the convergence check. Finally, useStochastic determines whether or not batch functions should be optimized using a stochastic gradient algorithm (using small batches), or using LBFGS (using the entire dataset).

OptParams can be controlled using breeze.config.Configuration, which we described earlier.

breeze.optimize.linear

We provide a DSL for solving linear programs, using Apache's Simplex Solver as the backend. This package isn't industrial strength yet by any means, but it's good for simple problems. The DSL is pretty simple:

import breeze.optimize.linear._
val lp = new LinearProgram()
import lp._
val x0 = Real()
val x1 = Real()
val x2 = Real()

val lpp =  ( (x0 +  x1 * 2 + x2 * 3 )
    subjectTo ( x0 * -1 + x1 + x2 <= 20)
    subjectTo ( x0 - x1 * 3 + x2 <= 30)
    subjectTo ( x0 <= 40 )
)

val result = maximize( lpp)

assert( norm(result.result - DenseVector(40.0,17.5,42.5), 2) < 1E-4)

We also have specialized routines for bipartite matching (KuhnMunkres and CompetitiveLinking) and flow problems.

Where to go next?

After reading this quickstart, you can go to other wiki pages, especially Linear Algebra Cheat-Sheet and Data Structures.

Review the following for example:

if you have not experienced or forgotten big-O and big-Omega and big-Theta notation to study the computational efficiency of algorithms.

ScaDaMaLe Course site and book

Let us visit an interactive visual cognitive tool for the basics ideas in linear regression:

Linear Regression by Hastie and Tibshirani

Chapter 3 of https://www.dataschool.io/15-hours-of-expert-machine-learning-videos/

The following video playlist is a very concise and thorough treatment of linear regression for those who have taken the 200-level linear algebra. Others can fully understand it with some effort and revisiting.

Linear Regression PlayList

Ridge regression has a Bayesian interpretation where the weights have a zero-mean Gaussian prior. See 7.5 in Murphy's Machine Learning: A Probabilistic Perspective for details.

Please take notes in mark-down if you want.

For latex math within markdown you can do the following for in-line maths: \(\mathbf{A}_{i,j} \in \mathbb{R}^1\). And to write maths in display mode do the following:

\[\mathbf{A} \in \mathbb{R}^{m \times d} \]

You will need to write such notes for your final project presentation!

Getting our hands dirty with Darren Wilkinson's blog on regression

Let's follow the exposition in:

You need to scroll down the fitst link embedded in iframe below to get to the section on Analysis of quantitative data with Descriptive statistics and Linear regression sub-sections (you can skip the earlier part that shows you how to run everything locally in spark-shell - try this on your own later).

Let's do this live now...

import breeze.stats.distributions._
def x = Gaussian(1.0,2.0).sample(10000)
val xRdd = sc.parallelize(x)
import breeze.stats.distributions._
x: IndexedSeq[Double]
xRdd: org.apache.spark.rdd.RDD[Double] = ParallelCollectionRDD[0] at parallelize at command-2971213210277124:3
println(xRdd.mean)
println(xRdd.sampleVariance)
0.9961211853107911
4.025384520599017
val xStats = xRdd.stats
xStats.mean
xStats.sampleVariance
xStats.sum
xStats: org.apache.spark.util.StatCounter = (count: 10000, mean: 0.996121, stdev: 2.006236, max: 8.326542, min: -6.840659)
res1: Double = 9961.21185310791
val x2 = Gaussian(0.0,1.0).sample(10000) // 10,000 Gaussian samples with mean 0.0 and std dev 1.0
val xx = x zip x2 // creating tuples { (x,x2)_1, ... , (x,x2)_10000}
val lp = xx map {p => 2.0*p._1 + 1.0*p._2 + 1.5} // { lp_i := (2.0*x + 1.0 * x2 + 1.5)_i, i=1,...,10000 }
val eps = Gaussian(0.0,1.0).sample(10000) // standrad normal errors
val y = (lp zip eps) map (p => p._1 + p._2)
val yx = (y zip xx) map (p => (p._1, p._2._1, p._2._2))
x2: IndexedSeq[Double] = Vector(0.1510498720110515, -0.21709023201809416, -0.9420189342233366, -0.6050521762158899, 0.48771393128636853, 0.027986752952643124, 0.08206698908429294, -0.7810931162704136, -1.2057806605697985, -0.9176042669882863, 1.1959113751272468, 0.5771223111098949, -0.5030579509564024, 0.05792512611966754, 2.0492117764647917, -1.6192400586380957, -0.28568171141353893, 1.662660432138664, -0.3053683539449641, 0.3879563181609168, -0.7733054017369991, -0.39556455561853454, 1.7717311537878704, 0.33232937623812936, -0.1392031424321576, -0.5587152832826312, -1.7575839385785728, -0.6579581256900572, 2.037190332203657, 0.03462069676057432, -0.3795037160416964, 0.4622268686186779, -1.0897313199516543, -1.6880936202156007, -0.19374927120525648, -0.5509651353004006, -1.7588836379571422, -0.28930357427256465, 0.4020360571731675, -1.6301541413671794, 0.5958281089725639, 0.366330814768569, 0.4073858014158006, 0.16855406345881346, -0.947375008877488, -1.301502215739479, 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(-2.9824782737280255,1.0721139408861649), (1.559154053243073,-0.7709696933298915), (1.7355575197273223,1.4262689270118047), (1.11638805377925,0.008052693380149429), (4.6951872993892,-0.7675924241217212), (2.737373852455214,-0.875355770610139), (-1.151456200240173,0.3318552144813144), (3.0152094819448543,0.47230162167225975), (2.0959843639444466,-0.28845007593399613), (0.33596546387727444,0.33674053005607557), (1.040331737541483,-1.2685836846998517), (2.431166696911837,0.9973713512813284), (2.230055598607015,-0.14095584542177128), (1.3700666149073755,0.6434211266970435), (-0.4327077332358864,-1.3166935231718915), (-1.6077594316454586,0.5010874593219053), (-2.3718964441684305,0.5400322253256449), (2.6760922672748455,0.1131615290866549), (1.460158508062642,1.1948743843705798), (4.289535800486267,-0.4068064171361299), (0.7168408537080622,-0.2145531753251343), (-0.354296028077995,-0.8414414845064078), (0.6348900562033981,-0.17448661922809763), (4.50175610250241,0.015039956542559319), (4.007289452214197,-2.00225473143416), (0.5029484622378626,0.7768533690748148), (1.6705288530684772,0.7280781053306761), (-1.9266086884168034,-0.6814357844622568), (0.6563298284821315,2.4398143015234925), (3.8936524199780114,-1.9715384636473667), (-0.5323653052192214,-1.089089720589046), (-2.187378645730113,-1.0771030789727833), (1.4490595169584695,-1.1187887124853761), (-4.570489383235827,0.26304747184316635), (0.15125945754562187,0.6104069218328998), (3.502660482621176,0.814212432670669), (-0.7485242949055997,-1.1311163095796626), (3.5175847260522777,-0.715657837824097), (1.292722602559689,0.11337791560485909), (-1.0688535529107246,1.1903117127474667), (2.610918918455355,0.8655118045637775), (2.165592336786331,-0.4786300318354617), (3.2180039450399307,1.1374241148097717), (2.3110620837831366,1.3574248394663742), (-1.2620670074181475,-0.59796895966422), (-2.022658500226865,0.5787074373907313), (0.4225942665282606,-1.4837192620796162), (-1.8746483642338414,0.15009771866713956), (1.3304121456690439,-1.0785198355458125), (2.528499056420297,0.43654174540174034), (-2.5920035883882417,1.367374206941478), (1.8434672245723738,1.1624833124548457), (2.099308858628433,1.4378845237950593), (-0.8157539314263724,-0.4752367281036082), (-0.5844201825108297,-0.6295231876858187), (3.6001251647036625,0.13609988490474167), (0.9750494830689591,1.451172421854568), (-1.591208358857827,-0.9690521636819287), (2.272688328123594,-0.4657652028114279), (1.088984838199552,-0.3272245138051527), (2.700650297482846,-0.3254730682226242), (0.29059088340060446,-1.1968451698216205), (-0.8790370032378447,-2.374605096166881), (4.604279856177609,1.4231065460066927), (2.722449227993615,0.3339627050188421), (3.587573251254368,-0.37529586334821136), (-1.4412229896551314,1.7121288810552737), (2.0753371457353946,0.7740341080806812), (1.1111154091929833,-0.08101997848273264), (1.7671887536692417,0.8171553719668059), (1.9408459883070575,1.004037394973044), (0.7804144409892885,0.22996069331921015), (-1.8543998116282898,-0.135350519278533), (6.042636547872292,-0.4727403129550938), (2.1280007672692847,-0.1182151974084787), (0.4471612263594835,-1.9468945045910213), (1.2505523478947802,0.4579087802822954), (0.6984945299477181,1.3836409234546432), (-0.8471775601094396,0.02325932498935564), (4.322477962324404,0.475495388508411), (1.4341612180258405,-0.37698432805620236), (6.239615258142803,-0.8219848732487407), (-3.1535278213087903,-1.3951694203634668), (-0.463940144432212,0.0484490852454009), (-0.14771318640324793,0.9222291689334502), (0.20282785933721803,1.5679464498188418), (1.8482316809367179,0.810147143385619), (1.464243976509526,1.9186942393210789), (-2.344895033686407,-0.2176761309409645), (-0.6222382474654642,1.497682278641026), (-2.028256489351115,-0.6745280698091511), (-1.8185091579263823,-0.14287398549911423), (0.7775757995485517,-0.6123313834457077), (2.208419884574348,0.5533479535312111), (-1.510931362400885,0.17525285583058028), (0.15702274793503757,0.26417401560092896), (-0.460045243107128,0.7989612854266647), (3.543882315893044,-0.6531854416899909), (1.1358671646312586,0.3890137678570137), (1.0004036793674747,1.5942398929174109), (-2.229985885404819,0.29843502966443813), (0.27723413696937793,0.28270288452527464), (-1.0586523471937253,-1.030296515196584), (-0.6053699726992356,0.29004278605641326), (-0.9059032244427896,1.1839066433022867), (0.30610586096155024,0.5617980143776449), (-1.1035109557285785,0.3177318190024553), (0.818395734988232,-0.17078152902760071), (1.2887245591289829,-0.4129031279462113), (3.228020724069559,1.6509715706618235), (0.6610048448754513,-0.27367425727559463), (1.5679633903647399,1.2450208243939591), (1.5877868046262307,1.4063428988232145), (1.9799774803293921,1.6639488103943056), (1.8297536930120843,0.4109699563209272), (-0.21778571324236595,-2.1509670233572784), (0.6433445252381844,0.2639495116581482), (-1.261874773876885,-0.9708523309574577), (-1.020712141743926,1.2588123216998128), (-0.942167556946186,-0.6395148239066109), (2.7320211668089156,-2.3731627585033115), (2.812558906168454,0.43524872907522616), (-0.056923496414450714,0.6328073362083871), (-0.6014131312820246,-0.2381862432808314), (-3.5196269653783325,0.40492896291344244), (-1.1067214502928073,-1.0527840343286374), (-0.4736116098154268,1.0689442908821987), (2.6403094933932953,0.789255581937264), (1.5982824524769197,1.1724902795494772), (-0.09123150857004858,1.2893390188349818), (0.3777640975590455,0.8926054903089587), (1.5757168418364564,1.4246842661952515), (-0.24202485980852528,0.21910907895561132), (4.589933486557021,0.34689263334132264), (-2.331742795642637,-0.5771627038699307), (1.0060513913917988,-0.04827308490054824), (-0.4295021770429881,-0.8361201294738408), (-0.21561647198666445,0.2776346366703466), (1.4993086132360396,-2.583216199463966), (1.0627822777545926,-0.5754336242709439), (-2.4095942089088482,-0.4740298729504418), (1.5975461609152366,0.45528050967309863), (2.1565799558529477,-0.937001723779216), (0.0962289023611611,0.12442585999261868), (2.7095641996945012,-1.037597020742512), (-0.9219208363686942,0.6656497732259127), (-1.0338058740520197,0.09718535082910094), (1.6364174103842437,0.472044663569549), (1.2274838964756027,0.01365815985041524), (-0.7303973452135653,0.21443946294874028), (1.6471043795729972,0.38540036725618015), (0.13612088488197083,0.7807770362857364), (-4.201610226957669,0.12940125757456059), (0.8225909001565422,-0.9556204076037894), (-0.9482388322224697,-1.0007190699745476), (-1.5523717842885172,-1.4238233782457508), (-1.4048827543540963,0.09834207753278863), (1.5338217310158921,-2.5447136959911605), (2.2987508128497063,0.1997331013963162), (-1.9069233483255275,1.2806574080505437), (-0.48017389975436475,0.9315316175761184), (3.708171200382932,-0.6394107818742375), (1.646362242992558,-1.4099227738716835), (5.344457888650813,-0.21682467720141205), (4.0401870066710455,-0.214248285713938...
val rddLR = sc.parallelize(yx)
rddLR.take(5)
rddLR: org.apache.spark.rdd.RDD[(Double, Double, Double)] = ParallelCollectionRDD[4] at parallelize at command-2971213210277128:1
res2: Array[(Double, Double, Double)] = Array((5.677461671611596,1.6983876233282715,0.1510498720110515), (6.5963106438672625,1.9306937118935266,-0.21709023201809416), (-6.457080480280965,-3.613579039093624,-0.9420189342233366), (5.725199404014689,1.4774128627063305,-0.6050521762158899), (5.2485124653727215,0.49536920319327216,0.48771393128636853))
val dfLR = rddLR.toDF("y","x1","x2")
dfLR.show
dfLR.show(5)
+-------------------+--------------------+--------------------+
|                  y|                  x1|                  x2|
+-------------------+--------------------+--------------------+
|  5.677461671611596|  1.6983876233282715|  0.1510498720110515|
| 6.5963106438672625|  1.9306937118935266|-0.21709023201809416|
| -6.457080480280965|  -3.613579039093624| -0.9420189342233366|
|  5.725199404014689|  1.4774128627063305| -0.6050521762158899|
| 5.2485124653727215| 0.49536920319327216| 0.48771393128636853|
|  6.147100844408568|   2.619266385545484|0.027986752952643124|
|-0.7268042607303868| -1.6216138344745752| 0.08206698908429294|
| 5.5363351738375695|  1.2511380715559544| -0.7810931162704136|
|-0.1828379004896784| -0.6891022233658615| -1.2057806605697985|
|  6.488199218865876|  2.7890847095863527| -0.9176042669882863|
| 1.3969322930903634| -0.8384317817611013|  1.1959113751272468|
|  1.468434023004454|-0.39702300426389736|  0.5771223111098949|
|-0.6234341966751746|-0.20341459413042506| -0.5030579509564024|
|  6.452061108539848|   1.940354690386933| 0.05792512611966754|
|  9.199371261060582|  3.1686700336304794|  2.0492117764647917|
|0.07256979343692907|-0.01571825151138...| -1.6192400586380957|
|  9.589528428542355|  3.5222633033548227|-0.28568171141353893|
| 1.1696257215909478| -1.7700416261712641|   1.662660432138664|
|-0.8138719762638745|  -1.276616299487233| -0.3053683539449641|
|  9.309926019422797|   2.847017612404211|  0.3879563181609168|
+-------------------+--------------------+--------------------+
only showing top 20 rows

+------------------+-------------------+--------------------+
|                 y|                 x1|                  x2|
+------------------+-------------------+--------------------+
| 5.677461671611596| 1.6983876233282715|  0.1510498720110515|
|6.5963106438672625| 1.9306937118935266|-0.21709023201809416|
|-6.457080480280965| -3.613579039093624| -0.9420189342233366|
| 5.725199404014689| 1.4774128627063305| -0.6050521762158899|
|5.2485124653727215|0.49536920319327216| 0.48771393128636853|
+------------------+-------------------+--------------------+
only showing top 5 rows

dfLR: org.apache.spark.sql.DataFrame = [y: double, x1: double ... 1 more field]
// importing for regression
import org.apache.spark.ml.regression.LinearRegression
import org.apache.spark.ml.linalg._

val lm = new LinearRegression
lm.explainParams
lm.getStandardization
lm.setStandardization(false)
lm.getStandardization
lm.explainParams
import org.apache.spark.ml.regression.LinearRegression
import org.apache.spark.ml.linalg._
lm: org.apache.spark.ml.regression.LinearRegression = linReg_fd18c4adb9af
res5: String =
aggregationDepth: suggested depth for treeAggregate (>= 2) (default: 2)
elasticNetParam: the ElasticNet mixing parameter, in range [0, 1]. For alpha = 0, the penalty is an L2 penalty. For alpha = 1, it is an L1 penalty (default: 0.0)
epsilon: The shape parameter to control the amount of robustness. Must be > 1.0. (default: 1.35)
featuresCol: features column name (default: features)
fitIntercept: whether to fit an intercept term (default: true)
labelCol: label column name (default: label)
loss: The loss function to be optimized. Supported options: squaredError, huber. (Default squaredError) (default: squaredError)
maxBlockSizeInMB: Maximum memory in MB for stacking input data into blocks. Data is stacked within partitions. If more than remaining data size in a partition then it is adjusted to the data size. Default 0.0 represents choosing optimal value, depends on specific algorithm. Must be >= 0. (default: 0.0)
maxIter: maximum number of iterations (>= 0) (default: 100)
predictionCol: prediction column name (default: prediction)
regParam: regularization parameter (>= 0) (default: 0.0)
solver: The solver algorithm for optimization. Supported options: auto, normal, l-bfgs. (Default auto) (default: auto)
standardization: whether to standardize the training features before fitting the model (default: true, current: false)
tol: the convergence tolerance for iterative algorithms (>= 0) (default: 1.0E-6)
weightCol: weight column name. If this is not set or empty, we treat all instance weights as 1.0 (undefined)
// Transform data frame to required format
val dflr = (dfLR map {row => (row.getDouble(0), 
           Vectors.dense(row.getDouble(1),row.getDouble(2)))}).
           toDF("label","features")
dflr.show(5)
+------------------+--------------------+
|             label|            features|
+------------------+--------------------+
| 5.677461671611596|[1.69838762332827...|
|6.5963106438672625|[1.93069371189352...|
|-6.457080480280965|[-3.6135790390936...|
| 5.725199404014689|[1.47741286270633...|
|5.2485124653727215|[0.49536920319327...|
+------------------+--------------------+
only showing top 5 rows

dflr: org.apache.spark.sql.DataFrame = [label: double, features: vector]
// Fit model
val fit = lm.fit(dflr)
fit.intercept
fit: org.apache.spark.ml.regression.LinearRegressionModel = LinearRegressionModel: uid=linReg_fd18c4adb9af, numFeatures=2
res8: Double = 1.4942320912612896
fit.coefficients
res9: org.apache.spark.ml.linalg.Vector = [1.9996093571014764,1.0144075351786204]
val summ = fit.summary
summ: org.apache.spark.ml.regression.LinearRegressionTrainingSummary = org.apache.spark.ml.regression.LinearRegressionTrainingSummary@b34e84f
summ.r2
res10: Double = 0.9436414660418528
summ.rootMeanSquaredError
res11: Double = 1.0026971017612039
summ.coefficientStandardErrors
res12: Array[Double] = Array(0.005018897596822849, 0.009968316877946075, 0.01123197045538135)
summ.pValues
res13: Array[Double] = Array(0.0, 0.0, 0.0)
summ.tValues
res14: Array[Double] = Array(398.4160502432455, 101.76317101464718, 133.03383384038267)
summ.predictions.show(5)
+------------------+--------------------+------------------+
|             label|            features|        prediction|
+------------------+--------------------+------------------+
| 5.677461671611596|[1.69838762332827...| 5.043570003209616|
|6.5963106438672625|[1.93069371189352...| 5.134647336087737|
|-6.457080480280965|[-3.6135790390936...|-6.687105473093168|
| 5.725199404014689|[1.47741286270633...| 3.834711189101326|
|5.2485124653727215|[0.49536920319327...|2.9795176720949392|
+------------------+--------------------+------------------+
only showing top 5 rows
summ.residuals.show(5)
+-------------------+
|          residuals|
+-------------------+
| 0.6338916684019802|
| 1.4616633077795251|
|0.23002499281220334|
|  1.890488214913363|
| 2.2689947932777823|
+-------------------+
only showing top 5 rows

This gives you more on doing generalised linear modelling in Scala. But let's go back to out pipeline using the power-plant data.

Exercise: Writing your own Spark program for the least squares fit

Your task is to use the syntactic sugar below to write your own linear regression function using reduce and broadcast operations

How would you write your own Spark program to find the least squares fit on the following 1000 data points in RDD rddLR, where the variable y is the response variable, and X1 and X2 are independent variables?

More precisely, find \(w_1, w_2\), such that,

\(\sum_{i=1}^{10} (w_1 X1_i + w_2 X2_i - y_i)^2\) is minimized.

Report \(w_1\), \(w_2\), and the Root Mean Square Error and submit code in Spark. Analyze the resulting algorithm in terms of all-to-all, one-to-all, and all-to-one communication patterns.

rddLR.count
res17: Long = 10000
rddLR.take(10)
res18: Array[(Double, Double, Double)] = Array((5.677461671611596,1.6983876233282715,0.1510498720110515), (6.5963106438672625,1.9306937118935266,-0.21709023201809416), (-6.457080480280965,-3.613579039093624,-0.9420189342233366), (5.725199404014689,1.4774128627063305,-0.6050521762158899), (5.2485124653727215,0.49536920319327216,0.48771393128636853), (6.147100844408568,2.619266385545484,0.027986752952643124), (-0.7268042607303868,-1.6216138344745752,0.08206698908429294), (5.5363351738375695,1.2511380715559544,-0.7810931162704136), (-0.1828379004896784,-0.6891022233658615,-1.2057806605697985), (6.488199218865876,2.7890847095863527,-0.9176042669882863))
val dfLR = rddLR.toDF("y","x1","x2")
dfLR.show(10)
+-------------------+-------------------+--------------------+
|                  y|                 x1|                  x2|
+-------------------+-------------------+--------------------+
|  5.677461671611596| 1.6983876233282715|  0.1510498720110515|
| 6.5963106438672625| 1.9306937118935266|-0.21709023201809416|
| -6.457080480280965| -3.613579039093624| -0.9420189342233366|
|  5.725199404014689| 1.4774128627063305| -0.6050521762158899|
| 5.2485124653727215|0.49536920319327216| 0.48771393128636853|
|  6.147100844408568|  2.619266385545484|0.027986752952643124|
|-0.7268042607303868|-1.6216138344745752| 0.08206698908429294|
| 5.5363351738375695| 1.2511380715559544| -0.7810931162704136|
|-0.1828379004896784|-0.6891022233658615| -1.2057806605697985|
|  6.488199218865876| 2.7890847095863527| -0.9176042669882863|
+-------------------+-------------------+--------------------+
only showing top 10 rows

dfLR: org.apache.spark.sql.DataFrame = [y: double, x1: double ... 1 more field]
rddLR.getNumPartitions
res21: Int = 2
rddLR.map( yx1x2 => (yx1x2._2, yx1x2._3, yx1x2._1) ).take(10)
res22: Array[(Double, Double, Double)] = Array((1.6983876233282715,0.1510498720110515,5.677461671611596), (1.9306937118935266,-0.21709023201809416,6.5963106438672625), (-3.613579039093624,-0.9420189342233366,-6.457080480280965), (1.4774128627063305,-0.6050521762158899,5.725199404014689), (0.49536920319327216,0.48771393128636853,5.2485124653727215), (2.619266385545484,0.027986752952643124,6.147100844408568), (-1.6216138344745752,0.08206698908429294,-0.7268042607303868), (1.2511380715559544,-0.7810931162704136,5.5363351738375695), (-0.6891022233658615,-1.2057806605697985,-0.1828379004896784), (2.7890847095863527,-0.9176042669882863,6.488199218865876))
import breeze.linalg.DenseVector
    val pts = rddLR.map( yx1x2 => DenseVector(yx1x2._2, yx1x2._3, yx1x2._1) ).cache
import breeze.linalg.DenseVector
pts: org.apache.spark.rdd.RDD[breeze.linalg.DenseVector[Double]] = MapPartitionsRDD[40] at map at command-2971213210277150:2

Now all we need to do is one-to-all and all-to-one broadcast of the gradient...

val w = DenseVector(0.0, 0.0, 0.0)
val w_bc = sc.broadcast(w)
val step = 0.1
val max_iter = 100

/*
YouTry: Fix the expressions for grad_w0, grad_w1 and grad_w2 to have w_bc.value be the same as that from ml lib's fit.coefficients
*/    
for (i <- 1 to max_iter) {
        val grad_w0 = pts.map(x => 2*(w_bc.value(0)*1.0 + w_bc.value(1)*x(0) + w_bc.value(2)*x(1) - x(2))*1.0).reduce(_+_)
        val grad_w1 = pts.map(x => 2*(w_bc.value(0)*1.0 + w_bc.value(1)*x(0) + w_bc.value(2)*x(1) - x(2))*x(0)).reduce(_+_)
        val grad_w2 = pts.map(x => 2*(w_bc.value(0)*1.0 + w_bc.value(1)*x(0) + w_bc.value(2)*x(1) - x(2))*x(1)).reduce(_+_)
        w_bc.value(0) = w_bc.value(0) - step*grad_w0
        w_bc.value(1) = w_bc.value(1) - step*grad_w1
        w_bc.value(2) = w_bc.value(2) - step*grad_w2
}
w: breeze.linalg.DenseVector[Double] = DenseVector(703602.5501372493, 2297216.693185762, 194396.78259181185)
w_bc: org.apache.spark.broadcast.Broadcast[breeze.linalg.DenseVector[Double]] = Broadcast(16)
step: Double = 0.1
max_iter: Int = 100
w_bc.value
res24: breeze.linalg.DenseVector[Double] = DenseVector(703602.5501372493, 2297216.693185762, 194396.78259181185)
fit.intercept
res25: Double = 1.4942320912612896
fit.coefficients
res26: org.apache.spark.ml.linalg.Vector = [1.9996093571014764,1.0144075351786204]

Computing each of the gradients requires an all-to-one communication (due to the .reduce(_+_)). There are two of these per iteration. Broadcasting the updated w_bc requires one to all communication.

ScaDaMaLe Course site and book

A more detailed deep dive

We will mostly be using ML algorithms already implemented in Spark's libraries and packages.

However, in order to innovate and devise new algorithms, we need to understand more about distributed linear algebra and optimisation algorithms.

  • read: http://arxiv.org/pdf/1509.02256.pdf (also see References and Appendix A).
  • and go through the notebooks prepended by '19x' on various Data Types for distributed linear algebra.

You may want to follow this course from Stanford for a guided deeper dive. * http://stanford.edu/~rezab/dao/ * see notes here: https://github.com/lamastex/scalable-data-science/blob/master/read/daosu.pdf

Communication Hierarchy

In addition to time and space complexity of an algorithm, in the distributed setting, we also need to take care of communication complexity.

Access rates fall sharply with distance.

  • roughly 50 x gap between reading from memory and reading from either disk or the network.

We must take this communication hierarchy into consideration when developing parallel and distributed algorithms.

Focusing on strategies to reduce communication costs.

  • access rates fall sharply with distance.
  • so this communication hierarchy needs to be accounted for when developing parallel and distributed algorithms.

Lessons:

  • parallelism makes our computation faster

  • but network communication slows us down

  • SOLUTION: perform parallel and in-memory computation.

  • Persisting in memory is a particularly attractive option when working with iterative algorithms that read the same data multiple times, as is the case in gradient descent.

  • Several machine learning algorithms are iterative!

  • Limits of multi-core scaling (powerful multicore machine with several CPUs, and a huge amount of RAM).

    • advantageous:
      • sidestep any network communication when working with a single multicore machine
      • can indeed handle fairly large data sets, and they're an attractive option in many settings.
    • disadvantages:
      • can be quite expensive (due to specialized hardware),
      • not as widely accessible as commodity computing nodes.
      • this approach does have scalability limitations, as we'll eventually hit a wall when the data grows large enough! This is not the case for a distributed environment (like the AWS EC2 cloud under the hood here).

Simple strategies for algorithms in a distributed setting: to reduce network communication, simply keep large objects local

  • In the big n, small d case for linear regression
    • we can solve the problem via a closed form solution.
    • And this requires us to communicate \(O(d)^2\) intermediate data.
    • the largest object in this example is our initial data, which we store in a distributed fashion and never communicate! This is a data parallel setting.
  • In the big n, big d case (n is the sample size and d is the number of features):
    • for linear regression.
      • we use gradient descent to iteratively train our model and are again in a data parallel setting.
      • At each iteration we communicate the current parameter vector \(w_i\) and the required \(O(d)\) communication is feasible even for fairly large d.
  • In the small n, small d case:
    • for ridge regression.
      • we can communicate the small data to all of the workers.
      • this is an example of a model parallel setting where we can train the model for each hyper-parameter in parallel.
  • Linear regression with big n and huge d is an example of both data and model parallelism.

In this setting, since our data is large, we must still store it across multiple machines. We can still use gradient descent, or stochastic variants of gradient descent to train our model, but we may not want to communicate the entire d dimensional parameter vector at each iteration, when we have 10s, or hundreds of millions of features. In this setting we often rely on sparsity to reduce the communication. So far we discussed how we can reduce communication by keeping large data local.

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

Why are we going through the basic distributed linear algebra Data Types?

This is to get you to be able to directly use them in a project or to roll your own algorithms.

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

Local vector in Scala

A local vector has integer-typed and 0-based indices and double-typed values, stored on a single machine.

MLlib supports two types of local vectors:

  • dense and
  • sparse.

A dense vector is backed by a double array representing its entry values, while a sparse vector is backed by two parallel arrays: indices and values.

For example, a vector (1.0, 0.0, 3.0) can be represented:

  • in dense format as [1.0, 0.0, 3.0] or
  • in sparse format as (3, [0, 2], [1.0, 3.0]), where 3 is the size of the vector.

The base class of local vectors is Vector, and we provide two implementations: DenseVector and SparseVector. We recommend using the factory methods implemented in Vectors to create local vectors. Refer to the Vector Scala docs and Vectors Scala docs for details on the API.

import org.apache.spark.mllib.linalg.{Vector, Vectors}

// Create a dense vector (1.0, 0.0, 3.0).
val dv: Vector = Vectors.dense(1.0, 0.0, 3.0)
import org.apache.spark.mllib.linalg.{Vector, Vectors}
dv: org.apache.spark.mllib.linalg.Vector = [1.0,0.0,3.0]
// Create a sparse vector (1.0, 0.0, 3.0) by specifying its indices and values corresponding to nonzero entries.
val sv1: Vector = Vectors.sparse(3, Array(0, 2), Array(1.0, 3.0))
sv1: org.apache.spark.mllib.linalg.Vector = (3,[0,2],[1.0,3.0])
// Create a sparse vector (1.0, 0.0, 3.0) by specifying its nonzero entries.
val sv2: Vector = Vectors.sparse(3, Seq((0, 1.0), (2, 3.0)))
sv2: org.apache.spark.mllib.linalg.Vector = (3,[0,2],[1.0,3.0])

Note: Scala imports scala.collection.immutable.Vector by default, so you have to import org.apache.spark.mllib.linalg.Vector explicitly to use MLlib’s Vector.

python: MLlib recognizes the following types as dense vectors:

  • NumPy’s array
  • Python’s list, e.g., [1, 2, 3]

and the following as sparse vectors:

We recommend using NumPy arrays over lists for efficiency, and using the factory methods implemented in Vectors to create sparse vectors.

Refer to the Vectors Python docs for more details on the API.

import numpy as np
import scipy.sparse as sps
from pyspark.mllib.linalg import Vectors

# Use a NumPy array as a dense vector.
dv1 = np.array([1.0, 0.0, 3.0])
# Use a Python list as a dense vector.
dv2 = [1.0, 0.0, 3.0]
# Create a SparseVector.
sv1 = Vectors.sparse(3, [0, 2], [1.0, 3.0])
# Use a single-column SciPy csc_matrix as a sparse vector.
sv2 = sps.csc_matrix((np.array([1.0, 3.0]), np.array([0, 2]), np.array([0, 2])), shape = (3, 1))
print (dv1)
print (dv2)
print (sv1)
print (sv2)
[1. 0. 3.]
[1.0, 0.0, 3.0]
(3,[0,2],[1.0,3.0])
  (0, 0)	1.0
  (2, 0)	3.0

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

Labeled point in Scala

A labeled point is a local vector, either dense or sparse, associated with a label/response. In MLlib, labeled points are used in supervised learning algorithms.

We use a double to store a label, so we can use labeled points in both regression and classification.

For binary classification, a label should be either 0 (negative) or 1 (positive). For multiclass classification, labels should be class indices starting from zero: 0, 1, 2, ....

A labeled point is represented by the case class LabeledPoint.

Refer to the LabeledPoint Scala docs for details on the API.

//import first
import org.apache.spark.mllib.linalg.Vectors
import org.apache.spark.mllib.regression.LabeledPoint
import org.apache.spark.mllib.linalg.Vectors
import org.apache.spark.mllib.regression.LabeledPoint
// Create a labeled point with a "positive" label and a dense feature vector.
val pos = LabeledPoint(1.0, Vectors.dense(1.0, 0.0, 3.0))
pos: org.apache.spark.mllib.regression.LabeledPoint = (1.0,[1.0,0.0,3.0])
// Create a labeled point with a "negative" label and a sparse feature vector.
val neg = LabeledPoint(0.0, Vectors.sparse(3, Array(0, 2), Array(1.0, 3.0)))
neg: org.apache.spark.mllib.regression.LabeledPoint = (0.0,(3,[0,2],[1.0,3.0]))

Sparse data in Scala

It is very common in practice to have sparse training data. MLlib supports reading training examples stored in LIBSVM format, which is the default format used by LIBSVM and LIBLINEAR. It is a text format in which each line represents a labeled sparse feature vector using the following format:

label index1:value1 index2:value2 ...

where the indices are one-based and in ascending order. After loading, the feature indices are converted to zero-based.

MLUtils.loadLibSVMFile reads training examples stored in LIBSVM format.

Refer to the MLUtils Scala docs for details on the API.

import org.apache.spark.mllib.regression.LabeledPoint
import org.apache.spark.mllib.util.MLUtils
import org.apache.spark.rdd.RDD

//val examples: RDD[LabeledPoint] = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt") // from prog guide but no such data here - can wget from github 
import org.apache.spark.mllib.regression.LabeledPoint
import org.apache.spark.mllib.util.MLUtils
import org.apache.spark.rdd.RDD

Load MNIST training and test datasets

Our datasets are vectors of pixels representing images of handwritten digits. For example:

Image of a digit Image of all 10 digits

display(dbutils.fs.ls("/datasets/sds/mnist-digits/data-001/mnist-digits-train.txt"))
path name size
dbfs:/datasets/sds/mnist-digits/data-001/mnist-digits-train.txt mnist-digits-train.txt 6.9430283e7
val examples: RDD[LabeledPoint] = MLUtils.loadLibSVMFile(sc, "/datasets/sds/mnist-digits/data-001/mnist-digits-train.txt")
examples: org.apache.spark.rdd.RDD[org.apache.spark.mllib.regression.LabeledPoint] = MapPartitionsRDD[246] at map at MLUtils.scala:87
examples.take(1)
res7: Array[org.apache.spark.mllib.regression.LabeledPoint] = Array((5.0,(780,[152,153,154,155,156,157,158,159,160,161,162,163,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,231,232,233,234,235,236,237,238,239,240,241,260,261,262,263,264,265,266,268,269,289,290,291,292,293,319,320,321,322,347,348,349,350,376,377,378,379,380,381,405,406,407,408,409,410,434,435,436,437,438,439,463,464,465,466,467,493,494,495,496,518,519,520,521,522,523,524,544,545,546,547,548,549,550,551,570,571,572,573,574,575,576,577,578,596,597,598,599,600,601,602,603,604,605,622,623,624,625,626,627,628,629,630,631,648,649,650,651,652,653,654,655,656,657,676,677,678,679,680,681,682,683],[3.0,18.0,18.0,18.0,126.0,136.0,175.0,26.0,166.0,255.0,247.0,127.0,30.0,36.0,94.0,154.0,170.0,253.0,253.0,253.0,253.0,253.0,225.0,172.0,253.0,242.0,195.0,64.0,49.0,238.0,253.0,253.0,253.0,253.0,253.0,253.0,253.0,253.0,251.0,93.0,82.0,82.0,56.0,39.0,18.0,219.0,253.0,253.0,253.0,253.0,253.0,198.0,182.0,247.0,241.0,80.0,156.0,107.0,253.0,253.0,205.0,11.0,43.0,154.0,14.0,1.0,154.0,253.0,90.0,139.0,253.0,190.0,2.0,11.0,190.0,253.0,70.0,35.0,241.0,225.0,160.0,108.0,1.0,81.0,240.0,253.0,253.0,119.0,25.0,45.0,186.0,253.0,253.0,150.0,27.0,16.0,93.0,252.0,253.0,187.0,249.0,253.0,249.0,64.0,46.0,130.0,183.0,253.0,253.0,207.0,2.0,39.0,148.0,229.0,253.0,253.0,253.0,250.0,182.0,24.0,114.0,221.0,253.0,253.0,253.0,253.0,201.0,78.0,23.0,66.0,213.0,253.0,253.0,253.0,253.0,198.0,81.0,2.0,18.0,171.0,219.0,253.0,253.0,253.0,253.0,195.0,80.0,9.0,55.0,172.0,226.0,253.0,253.0,253.0,253.0,244.0,133.0,11.0,136.0,253.0,253.0,253.0,212.0,135.0,132.0,16.0])))

Display our data. Each image has the true label (the label column) and a vector of features which represent pixel intensities (see below for details of what is in training).

display(examples.toDF) // covert to DataFrame and display for convenient db visualization

The pixel intensities are represented in features as a sparse vector, for example the first observation, as seen in row 1 of the output to display(training) below, has label as 5, i.e. the hand-written image is for the number 5. And this hand-written image is the following sparse vector (just click the triangle to the left of the feature in first row to see the following):

type: 0
size: 780
indices: [152,153,155,...,682,683]
values: [3, 18, 18,18,126,...,132,16]

Here

  • type: 0 says we hve a sparse vector.
  • size: 780 says the vector has 780 indices in total
  • these indices from 0,...,779 are a unidimensional indexing of the two-dimensional array of pixels in the image
  • indices: [152,153,155,...,682,683] are the indices from the [0,1,...,779] possible indices with non-zero values
    • a value is an integer encoding the gray-level at the pixel index
  • values: [3, 18, 18,18,126,...,132,16] are the actual gray level values, for example:
    • at pixed index 152 the gray-level value is 3,
    • at index 153 the gray-level value is 18,
    • ..., and finally at
    • at index 683 the gray-level value is 18

We could also use the following method as done in notebook 016_* already.

val training = spark.read.format("libsvm")
                    .option("numFeatures", "780")
                    .load("/datasets/sds/mnist-digits/data-001/mnist-digits-train.txt")
training: org.apache.spark.sql.DataFrame = [label: double, features: vector]
display(training)


Labeled point in Python

A labeled point is represented by LabeledPoint.

Refer to the LabeledPoint Python docs for more details on the API.

# import first
from pyspark.mllib.linalg import SparseVector
from pyspark.mllib.regression import LabeledPoint

# Create a labeled point with a positive label and a dense feature vector.
pos = LabeledPoint(1.0, [1.0, 0.0, 3.0])

# Create a labeled point with a negative label and a sparse feature vector.
neg = LabeledPoint(0.0, SparseVector(3, [0, 2], [1.0, 3.0]))

Sparse data in Python

MLUtils.loadLibSVMFile reads training examples stored in LIBSVM format.

Refer to the MLUtils Python docs for more details on the API.

from pyspark.mllib.util import MLUtils

# examples = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt") #from prog guide but no such data here - can wget from github 
examples = MLUtils.loadLibSVMFile(sc, "/datasets/sds/mnist-digits/data-001/mnist-digits-train.txt")
examples.take(1)
res11: Array[org.apache.spark.mllib.regression.LabeledPoint] = Array((5.0,(780,[152,153,154,155,156,157,158,159,160,161,162,163,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,231,232,233,234,235,236,237,238,239,240,241,260,261,262,263,264,265,266,268,269,289,290,291,292,293,319,320,321,322,347,348,349,350,376,377,378,379,380,381,405,406,407,408,409,410,434,435,436,437,438,439,463,464,465,466,467,493,494,495,496,518,519,520,521,522,523,524,544,545,546,547,548,549,550,551,570,571,572,573,574,575,576,577,578,596,597,598,599,600,601,602,603,604,605,622,623,624,625,626,627,628,629,630,631,648,649,650,651,652,653,654,655,656,657,676,677,678,679,680,681,682,683],[3.0,18.0,18.0,18.0,126.0,136.0,175.0,26.0,166.0,255.0,247.0,127.0,30.0,36.0,94.0,154.0,170.0,253.0,253.0,253.0,253.0,253.0,225.0,172.0,253.0,242.0,195.0,64.0,49.0,238.0,253.0,253.0,253.0,253.0,253.0,253.0,253.0,253.0,251.0,93.0,82.0,82.0,56.0,39.0,18.0,219.0,253.0,253.0,253.0,253.0,253.0,198.0,182.0,247.0,241.0,80.0,156.0,107.0,253.0,253.0,205.0,11.0,43.0,154.0,14.0,1.0,154.0,253.0,90.0,139.0,253.0,190.0,2.0,11.0,190.0,253.0,70.0,35.0,241.0,225.0,160.0,108.0,1.0,81.0,240.0,253.0,253.0,119.0,25.0,45.0,186.0,253.0,253.0,150.0,27.0,16.0,93.0,252.0,253.0,187.0,249.0,253.0,249.0,64.0,46.0,130.0,183.0,253.0,253.0,207.0,2.0,39.0,148.0,229.0,253.0,253.0,253.0,250.0,182.0,24.0,114.0,221.0,253.0,253.0,253.0,253.0,201.0,78.0,23.0,66.0,213.0,253.0,253.0,253.0,253.0,198.0,81.0,2.0,18.0,171.0,219.0,253.0,253.0,253.0,253.0,195.0,80.0,9.0,55.0,172.0,226.0,253.0,253.0,253.0,253.0,244.0,133.0,11.0,136.0,253.0,253.0,253.0,212.0,135.0,132.0,16.0])))

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

Local Matrix in Scala

A local matrix has integer-typed row and column indices and double-typed values, stored on a single machine. MLlib supports:

  • dense matrices, whose entry values are stored in a single double array in column-major order, and
  • sparse matrices, whose non-zero entry values are stored in the Compressed Sparse Column (CSC) format in column-major order.

For example, the following dense matrix: \[ \begin{pmatrix} 1.0 & 2.0 \\ 3.0 & 4.0 \\ 5.0 & 6.0 \end{pmatrix} \] is stored in a one-dimensional array [1.0, 3.0, 5.0, 2.0, 4.0, 6.0] with the matrix size (3, 2).

The base class of local matrices is Matrix, and we provide two implementations: DenseMatrix, and SparseMatrix. We recommend using the factory methods implemented in Matrices to create local matrices. Remember, local matrices in MLlib are stored in column-major order.

Refer to the Matrix Scala docs and Matrices Scala docs for details on the API.

Int.MaxValue // note the largest value an index can take
res0: Int = 2147483647
import org.apache.spark.mllib.linalg.{Matrix, Matrices}

// Create a dense matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0))
val dm: Matrix = Matrices.dense(3, 2, Array(1.0, 3.0, 5.0, 2.0, 4.0, 6.0))
import org.apache.spark.mllib.linalg.{Matrix, Matrices}
dm: org.apache.spark.mllib.linalg.Matrix =
1.0  2.0
3.0  4.0
5.0  6.0

Next, let us create the following sparse local matrix: \[ \begin{pmatrix} 9.0 & 0.0 \\ 0.0 & 8.0 \\ 0.0 & 6.0 \end{pmatrix} \]

// Create a sparse matrix ((9.0, 0.0), (0.0, 8.0), (0.0, 6.0))
val sm: Matrix = Matrices.sparse(3, 2, Array(0, 1, 3), Array(0, 2, 1), Array(9, 6, 8))
sm: org.apache.spark.mllib.linalg.Matrix =
3 x 2 CSCMatrix
(0,0) 9.0
(2,1) 6.0
(1,1) 8.0

Local Matrix in Python

The base class of local matrices is Matrix, and we provide two implementations: DenseMatrix, and SparseMatrix. We recommend using the factory methods implemented in Matrices to create local matrices. Remember, local matrices in MLlib are stored in column-major order.

Refer to the Matrix Python docs and Matrices Python docs for more details on the API.

from pyspark.mllib.linalg import Matrix, Matrices

# Create a dense matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0))
dm2 = Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])
dm2
# Create a sparse matrix ((9.0, 0.0), (0.0, 8.0), (0.0, 6.0))
sm = Matrices.sparse(3, 2, [0, 1, 3], [0, 2, 1], [9, 6, 8])
sm

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

Distributed matrix in Scala

A distributed matrix has long-typed row and column indices and double-typed values, stored distributively in one or more RDDs.

It is very important to choose the right format to store large and distributed matrices. Converting a distributed matrix to a different format may require a global shuffle, which is quite expensive.

Three types of distributed matrices have been implemented so far.

  1. The basic type is called RowMatrix.
  • A RowMatrix is a row-oriented distributed matrix without meaningful row indices, e.g., a collection of feature vectors. It is backed by an RDD of its rows, where each row is a local vector.
  • We assume that the number of columns is not huge for a RowMatrix so that a single local vector can be reasonably communicated to the driver and can also be stored / operated on using a single node.
  • An IndexedRowMatrix is similar to a RowMatrix but with row indices, which can be used for identifying rows and executing joins.
  • A CoordinateMatrix is a distributed matrix stored in coordinate list (COO) format, backed by an RDD of its entries.

Note

The underlying RDDs of a distributed matrix must be deterministic, because we cache the matrix size. In general the use of non-deterministic RDDs can lead to errors.

Remark: there is a huge difference in the orders of magnitude between the maximum size of local versus distributed matrices!

print(Long.MaxValue.toDouble, Int.MaxValue.toDouble, Long.MaxValue.toDouble / Int.MaxValue.toDouble) // index ranges and ratio for local and distributed matrices

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

RowMatrix in Scala

A RowMatrix is a row-oriented distributed matrix without meaningful row indices, backed by an RDD of its rows, where each row is a local vector. Since each row is represented by a local vector, the number of columns is limited by the integer range but it should be much smaller in practice.

A RowMatrix can be created from an RDD[Vector] instance. Then we can compute its column summary statistics and decompositions.

Refer to the RowMatrix Scala docs for details on the API.

import org.apache.spark.mllib.linalg.{Vector, Vectors}
import org.apache.spark.mllib.linalg.distributed.RowMatrix
import org.apache.spark.mllib.linalg.{Vector, Vectors}
import org.apache.spark.mllib.linalg.distributed.RowMatrix
val rows: RDD[Vector] = sc.parallelize(Array(Vectors.dense(12.0, -51.0, 4.0), Vectors.dense(6.0, 167.0, -68.0), Vectors.dense(-4.0, 24.0, -41.0))) // an RDD of local vectors
rows: org.apache.spark.rdd.RDD[org.apache.spark.mllib.linalg.Vector] = ParallelCollectionRDD[3670] at parallelize at command-2972105651606776:1
// Create a RowMatrix from an RDD[Vector].
val mat: RowMatrix = new RowMatrix(rows)
mat: org.apache.spark.mllib.linalg.distributed.RowMatrix = org.apache.spark.mllib.linalg.distributed.RowMatrix@75c66624
mat.rows.collect
res0: Array[org.apache.spark.mllib.linalg.Vector] = Array([12.0,-51.0,4.0], [6.0,167.0,-68.0], [-4.0,24.0,-41.0])
// Get its size.
val m = mat.numRows()
val n = mat.numCols()
m: Long = 3
n: Long = 3
// QR decomposition
val qrResult = mat.tallSkinnyQR(true)
qrResult: org.apache.spark.mllib.linalg.QRDecomposition[org.apache.spark.mllib.linalg.distributed.RowMatrix,org.apache.spark.mllib.linalg.Matrix] =
QRDecomposition(org.apache.spark.mllib.linalg.distributed.RowMatrix@34f5da4f,14.0  21.0                 -14.0
0.0   -174.99999999999997  70.00000000000001
0.0   0.0                  -35.000000000000014  )
qrResult.R
res1: org.apache.spark.mllib.linalg.Matrix =
14.0  21.0                 -14.0
0.0   -174.99999999999997  70.00000000000001
0.0   0.0                  -35.000000000000014


RowMatrix in Python

A RowMatrix can be created from an RDD of vectors.

Refer to the RowMatrix Python docs for more details on the API.

from pyspark.mllib.linalg.distributed import RowMatrix

# Create an RDD of vectors.
rows = sc.parallelize([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])

# Create a RowMatrix from an RDD of vectors.
mat = RowMatrix(rows)

# Get its size.
m = mat.numRows()  # 4
n = mat.numCols()  # 3
print (m,'x',n)

# Get the rows as an RDD of vectors again.
rowsRDD = mat.rows
4 x 3

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

IndexedRowMatrix in Scala

An IndexedRowMatrix is similar to a RowMatrix but with meaningful row indices. It is backed by an RDD of indexed rows, so that each row is represented by its index (long-typed) and a local vector.

An IndexedRowMatrix can be created from an RDD[IndexedRow] instance, where IndexedRow is a wrapper over (Long, Vector). An IndexedRowMatrix can be converted to a RowMatrix by dropping its row indices.

Refer to the IndexedRowMatrix Scala docs for details on the API.

import org.apache.spark.mllib.linalg.{Vector, Vectors}
import org.apache.spark.mllib.linalg.distributed.{IndexedRow, IndexedRowMatrix, RowMatrix}
import org.apache.spark.mllib.linalg.{Vector, Vectors}
import org.apache.spark.mllib.linalg.distributed.{IndexedRow, IndexedRowMatrix, RowMatrix}
Vector(12.0, -51.0, 4.0) // note Vector is a scala collection
res0: scala.collection.immutable.Vector[Double] = Vector(12.0, -51.0, 4.0)
Vectors.dense(12.0, -51.0, 4.0) // while this is a mllib.linalg.Vector
res1: org.apache.spark.mllib.linalg.Vector = [12.0,-51.0,4.0]
val rows: RDD[IndexedRow] = sc.parallelize(Array(IndexedRow(2, Vectors.dense(1,3)), IndexedRow(4, Vectors.dense(4,5)))) // an RDD of indexed rows
rows: org.apache.spark.rdd.RDD[org.apache.spark.mllib.linalg.distributed.IndexedRow] = ParallelCollectionRDD[3685] at parallelize at command-2972105651607186:1
// Create an IndexedRowMatrix from an RDD[IndexedRow].
val mat: IndexedRowMatrix = new IndexedRowMatrix(rows)
mat: org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix = org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix@300e1e99
// Get its size.
val m = mat.numRows()
val n = mat.numCols()
m: Long = 5
n: Long = 2
// Drop its row indices.
val rowMat: RowMatrix = mat.toRowMatrix()
rowMat: org.apache.spark.mllib.linalg.distributed.RowMatrix = org.apache.spark.mllib.linalg.distributed.RowMatrix@425fc4a2
rowMat.rows.collect()
res2: Array[org.apache.spark.mllib.linalg.Vector] = Array([1.0,3.0], [4.0,5.0])

IndexedRowMatrix in Python

An IndexedRowMatrix can be created from an RDD of IndexedRows, where IndexedRow is a wrapper over (long, vector). An IndexedRowMatrix can be converted to a RowMatrix by dropping its row indices.

Refer to the IndexedRowMatrix Python docs for more details on the API.

from pyspark.mllib.linalg.distributed import IndexedRow, IndexedRowMatrix

# Create an RDD of indexed rows.
#   - This can be done explicitly with the IndexedRow class:
indexedRows = sc.parallelize([IndexedRow(0, [1, 2, 3]),
                              IndexedRow(1, [4, 5, 6]),
                              IndexedRow(2, [7, 8, 9]),
                              IndexedRow(3, [10, 11, 12])])

#   - or by using (long, vector) tuples:
indexedRows = sc.parallelize([(0, [1, 2, 3]), (1, [4, 5, 6]),
                              (2, [7, 8, 9]), (3, [10, 11, 12])])

# Create an IndexedRowMatrix from an RDD of IndexedRows.
mat = IndexedRowMatrix(indexedRows)

# Get its size.
m = mat.numRows()  # 4
n = mat.numCols()  # 3
print (m,n)

# Get the rows as an RDD of IndexedRows.
rowsRDD = mat.rows

# Convert to a RowMatrix by dropping the row indices.
rowMat = mat.toRowMatrix()

# Convert to a CoordinateMatrix.
coordinateMat = mat.toCoordinateMatrix()

# Convert to a BlockMatrix.
blockMat = mat.toBlockMatrix()
4 3

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

CoordinateMatrix in Scala

A CoordinateMatrix is a distributed matrix backed by an RDD of its entries. Each entry is a tuple of (i: Long, j: Long, value: Double), where i is the row index, j is the column index, and value is the entry value. A CoordinateMatrix should be used only when both dimensions of the matrix are huge and the matrix is very sparse.

A CoordinateMatrix can be created from an RDD[MatrixEntry] instance, where MatrixEntry is a wrapper over (Long, Long, Double). A CoordinateMatrix can be converted to an IndexedRowMatrix with sparse rows by calling toIndexedRowMatrix. Other computations for CoordinateMatrix are not currently supported.

Refer to the CoordinateMatrix Scala docs for details on the API.

import org.apache.spark.mllib.linalg.distributed.{CoordinateMatrix, MatrixEntry}
import org.apache.spark.mllib.linalg.distributed.{CoordinateMatrix, MatrixEntry}
val entries: RDD[MatrixEntry] = sc.parallelize(Array(MatrixEntry(0, 0, 1.2), MatrixEntry(1, 0, 2.1), MatrixEntry(6, 1, 3.7))) // an RDD of matrix entries
entries: org.apache.spark.rdd.RDD[org.apache.spark.mllib.linalg.distributed.MatrixEntry] = ParallelCollectionRDD[3712] at parallelize at command-2972105651606627:1
// Create a CoordinateMatrix from an RDD[MatrixEntry].
val mat: CoordinateMatrix = new CoordinateMatrix(entries)
mat: org.apache.spark.mllib.linalg.distributed.CoordinateMatrix = org.apache.spark.mllib.linalg.distributed.CoordinateMatrix@56954954
// Get its size.
val m = mat.numRows()
val n = mat.numCols()
m: Long = 7
n: Long = 2
// Convert it to an IndexRowMatrix whose rows are sparse vectors.
val indexedRowMatrix = mat.toIndexedRowMatrix()
indexedRowMatrix: org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix = org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix@45570b82
indexedRowMatrix.rows.collect()
res0: Array[org.apache.spark.mllib.linalg.distributed.IndexedRow] = Array(IndexedRow(0,(2,[0],[1.2])), IndexedRow(1,(2,[0],[2.1])), IndexedRow(6,(2,[1],[3.7])))

CoordinateMatrix in Scala

A CoordinateMatrix can be created from an RDD of MatrixEntry entries, where MatrixEntry is a wrapper over (long, long, float). A CoordinateMatrix can be converted to a RowMatrix by calling toRowMatrix, or to an IndexedRowMatrix with sparse rows by calling toIndexedRowMatrix.

Refer to the CoordinateMatrix Python docs for more details on the API.

from pyspark.mllib.linalg.distributed import CoordinateMatrix, MatrixEntry

# Create an RDD of coordinate entries.
#   - This can be done explicitly with the MatrixEntry class:
entries = sc.parallelize([MatrixEntry(0, 0, 1.2), MatrixEntry(1, 0, 2.1), MatrixEntry(6, 1, 3.7)])

#   - or using (long, long, float) tuples:
entries = sc.parallelize([(0, 0, 1.2), (1, 0, 2.1), (2, 1, 3.7)])

# Create an CoordinateMatrix from an RDD of MatrixEntries.
mat = CoordinateMatrix(entries)

# Get its size.
m = mat.numRows()  # 3
n = mat.numCols()  # 2
print (m,n)

# Get the entries as an RDD of MatrixEntries.
entriesRDD = mat.entries

# Convert to a RowMatrix.
rowMat = mat.toRowMatrix()

# Convert to an IndexedRowMatrix.
indexedRowMat = mat.toIndexedRowMatrix()

# Convert to a BlockMatrix.
blockMat = mat.toBlockMatrix()
3 2

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

BlockMatrix in Scala

A BlockMatrix is a distributed matrix backed by an RDD of MatrixBlocks, where a MatrixBlock is a tuple of ((Int, Int), Matrix), where the (Int, Int) is the index of the block, and Matrix is the sub-matrix at the given index with size rowsPerBlock x colsPerBlock. BlockMatrix supports methods such as add and multiply with another BlockMatrix. BlockMatrix also has a helper function validate which can be used to check whether the BlockMatrix is set up properly.

A BlockMatrix can be most easily created from an IndexedRowMatrix or CoordinateMatrix by calling toBlockMatrix. toBlockMatrix creates blocks of size 1024 x 1024 by default. Users may change the block size by supplying the values through toBlockMatrix(rowsPerBlock, colsPerBlock).

Refer to the BlockMatrix Scala docs for details on the API.

//import org.apache.spark.mllib.linalg.{Matrix, Matrices}
import org.apache.spark.mllib.linalg.distributed.{BlockMatrix, CoordinateMatrix, MatrixEntry}
import org.apache.spark.mllib.linalg.distributed.{BlockMatrix, CoordinateMatrix, MatrixEntry}
val entries: RDD[MatrixEntry] = sc.parallelize(Array(MatrixEntry(0, 0, 1.2), MatrixEntry(1, 0, 2.1), MatrixEntry(6, 1, 3.7))) // an RDD of matrix entries
entries: org.apache.spark.rdd.RDD[org.apache.spark.mllib.linalg.distributed.MatrixEntry] = ParallelCollectionRDD[3746] at parallelize at command-2972105651607062:1
// Create a CoordinateMatrix from an RDD[MatrixEntry].
val coordMat: CoordinateMatrix = new CoordinateMatrix(entries)
coordMat: org.apache.spark.mllib.linalg.distributed.CoordinateMatrix = org.apache.spark.mllib.linalg.distributed.CoordinateMatrix@161a1942
// Transform the CoordinateMatrix to a BlockMatrix
val matA: BlockMatrix = coordMat.toBlockMatrix().cache()
matA: org.apache.spark.mllib.linalg.distributed.BlockMatrix = org.apache.spark.mllib.linalg.distributed.BlockMatrix@1ddf85ce
// Validate whether the BlockMatrix is set up properly. Throws an Exception when it is not valid.
// Nothing happens if it is valid.
matA.validate()
// Calculate A^T A.
val ata = matA.transpose.multiply(matA)
ata: org.apache.spark.mllib.linalg.distributed.BlockMatrix = org.apache.spark.mllib.linalg.distributed.BlockMatrix@18c0eeca
ata.blocks.collect()
res1: Array[((Int, Int), org.apache.spark.mllib.linalg.Matrix)] =
Array(((0,0),5.85  0.0
0.0   13.690000000000001  ))
ata.toLocalMatrix()
res2: org.apache.spark.mllib.linalg.Matrix =
5.85  0.0
0.0   13.690000000000001

BlockMatrix in Scala

A BlockMatrix can be created from an RDD of sub-matrix blocks, where a sub-matrix block is a ((blockRowIndex, blockColIndex), sub-matrix) tuple.

Refer to the BlockMatrix Python docs for more details on the API.

from pyspark.mllib.linalg import Matrices
from pyspark.mllib.linalg.distributed import BlockMatrix

# Create an RDD of sub-matrix blocks.
blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
                         ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])

# Create a BlockMatrix from an RDD of sub-matrix blocks.
mat = BlockMatrix(blocks, 3, 2)

# Get its size.
m = mat.numRows() # 6
n = mat.numCols() # 2
print (m,n)

# Get the blocks as an RDD of sub-matrix blocks.
blocksRDD = mat.blocks

# Convert to a LocalMatrix.
localMat = mat.toLocalMatrix()

# Convert to an IndexedRowMatrix.
indexedRowMat = mat.toIndexedRowMatrix()

# Convert to a CoordinateMatrix.
coordinateMat = mat.toCoordinateMatrix()
6 2

ScaDaMaLe Course site and book

Power Plant ML Pipeline Application

This is an end-to-end example of using a number of different machine learning algorithms to solve a supervised regression problem.

Table of Contents

  • Step 1: Business Understanding
  • Step 2: Load Your Data
  • Step 3: Explore Your Data
  • Step 4: Visualize Your Data
  • Step 5: Data Preparation
  • Step 6: Data Modeling
  • Step 7: Tuning and Evaluation
  • Step 8: Deployment

We are trying to predict power output given a set of readings from various sensors in a gas-fired power generation plant. Power generation is a complex process, and understanding and predicting power output is an important element in managing a plant and its connection to the power grid.

More information about Peaker or Peaking Power Plants can be found on Wikipedia https://en.wikipedia.org/wiki/Peakingpowerplant

Given this business problem, we need to translate it to a Machine Learning task. The ML task is regression since the label (or target) we are trying to predict is numeric.

The example data is provided by UCI at UCI Machine Learning Repository Combined Cycle Power Plant Data Set

You can read the background on the UCI page, but in summary we have collected a number of readings from sensors at a Gas Fired Power Plant

(also called a Peaker Plant) and now we want to use those sensor readings to predict how much power the plant will generate.

More information about Machine Learning with Spark can be found in the Spark MLLib Programming Guide

Please note this example only works with Spark version 1.4 or higher



To Rerun Steps 1-4 done in the notebook at:

  • Workspace -> PATH_TO -> 009_PowerPlantPipeline_01ETLEDA]

just run the following command as shown in the cell below:

%run "/PATH_TO/009_PowerPlantPipeline_01ETLEDA"
  • Note: If you already evaluated the %run ... command above then:

    • first delete the cell by pressing on x on the top-right corner of the cell and
    • revaluate the run command above.
"../009_PowerPlantPipeline_01ETLEDA" 


Now we will do the following Steps:

Step 5: Data Preparation,

Step 6: Modeling, and

Step 7: Tuning and Evaluation

We will do Step 8: Deployment later after we get introduced to SparkStreaming.

Step 5: Data Preparation

The next step is to prepare the data. Since all of this data is numeric and consistent, this is a simple task for us today.

We will need to convert the predictor features from columns to Feature Vectors using the org.apache.spark.ml.feature.VectorAssembler

The VectorAssembler will be the first step in building our ML pipeline.

res2: Int = 301
//Let's quickly recall the schema and make sure our table is here now
table("power_plant_table").printSchema
root
 |-- AT: double (nullable = true)
 |-- V: double (nullable = true)
 |-- AP: double (nullable = true)
 |-- RH: double (nullable = true)
 |-- PE: double (nullable = true)
path name size
dbfs:/databricks-datasets/power-plant/data/Sheet1.tsv Sheet1.tsv 308693.0
dbfs:/databricks-datasets/power-plant/data/Sheet2.tsv Sheet2.tsv 308693.0
dbfs:/databricks-datasets/power-plant/data/Sheet3.tsv Sheet3.tsv 308693.0
dbfs:/databricks-datasets/power-plant/data/Sheet4.tsv Sheet4.tsv 308693.0
dbfs:/databricks-datasets/power-plant/data/Sheet5.tsv Sheet5.tsv 308693.0
powerPlantRDD: org.apache.spark.rdd.RDD[String] = /databricks-datasets/power-plant/data/Sheet1.tsv MapPartitionsRDD[1] at textFile at command-1267216879634554:1
powerPlantDF // make sure we have the DataFrame too
res82: org.apache.spark.sql.DataFrame = [AT: double, V: double ... 3 more fields]
AT	V	AP	RH	PE
14.96	41.76	1024.07	73.17	463.26
25.18	62.96	1020.04	59.08	444.37
5.11	39.4	1012.16	92.14	488.56
20.86	57.32	1010.24	76.64	446.48
powerPlantDF: org.apache.spark.sql.DataFrame = [AT: double, V: double ... 3 more fields]
root
 |-- AT: double (nullable = true)
 |-- V: double (nullable = true)
 |-- AP: double (nullable = true)
 |-- RH: double (nullable = true)
 |-- PE: double (nullable = true)
import org.apache.spark.ml.feature.VectorAssembler

// make a DataFrame called dataset from the table
val dataset = sqlContext.table("power_plant_table") 

val vectorizer =  new VectorAssembler()
                      .setInputCols(Array("AT", "V", "AP", "RH"))
                      .setOutputCol("features")
import org.apache.spark.ml.feature.VectorAssembler
dataset: org.apache.spark.sql.DataFrame = [AT: double, V: double ... 3 more fields]
vectorizer: org.apache.spark.ml.feature.VectorAssembler = VectorAssembler: uid=vecAssembler_ea4ed428c7e4, handleInvalid=error, numInputCols=4
res9: Long = 9568
+-----+-----+-------+-----+------+
|   AT|    V|     AP|   RH|    PE|
+-----+-----+-------+-----+------+
|14.96|41.76|1024.07|73.17|463.26|
|25.18|62.96|1020.04|59.08|444.37|
| 5.11| 39.4|1012.16|92.14|488.56|
|20.86|57.32|1010.24|76.64|446.48|
|10.82| 37.5|1009.23|96.62| 473.9|
|26.27|59.44|1012.23|58.77|443.67|
|15.89|43.96|1014.02|75.24|467.35|
| 9.48|44.71|1019.12|66.43|478.42|
|14.64| 45.0|1021.78|41.25|475.98|
|11.74|43.56|1015.14|70.72| 477.5|
+-----+-----+-------+-----+------+
only showing top 10 rows
AT V AP RH PE
14.96 41.76 1024.07 73.17 463.26
25.18 62.96 1020.04 59.08 444.37
5.11 39.4 1012.16 92.14 488.56
20.86 57.32 1010.24 76.64 446.48
10.82 37.5 1009.23 96.62 473.9
26.27 59.44 1012.23 58.77 443.67
15.89 43.96 1014.02 75.24 467.35
9.48 44.71 1019.12 66.43 478.42
14.64 45.0 1021.78 41.25 475.98
11.74 43.56 1015.14 70.72 477.5
17.99 43.72 1008.64 75.04 453.02
20.14 46.93 1014.66 64.22 453.99
24.34 73.5 1011.31 84.15 440.29
25.71 58.59 1012.77 61.83 451.28
26.19 69.34 1009.48 87.59 433.99
21.42 43.79 1015.76 43.08 462.19
18.21 45.0 1022.86 48.84 467.54
11.04 41.74 1022.6 77.51 477.2
14.45 52.75 1023.97 63.59 459.85
13.97 38.47 1015.15 55.28 464.3
17.76 42.42 1009.09 66.26 468.27
5.41 40.07 1019.16 64.77 495.24
7.76 42.28 1008.52 83.31 483.8
27.23 63.9 1014.3 47.19 443.61
27.36 48.6 1003.18 54.93 436.06
27.47 70.72 1009.97 74.62 443.25
14.6 39.31 1011.11 72.52 464.16
7.91 39.96 1023.57 88.44 475.52
5.81 35.79 1012.14 92.28 484.41
30.53 65.18 1012.69 41.85 437.89
23.87 63.94 1019.02 44.28 445.11
26.09 58.41 1013.64 64.58 438.86
29.27 66.85 1011.11 63.25 440.98
27.38 74.16 1010.08 78.61 436.65
24.81 63.94 1018.76 44.51 444.26
12.75 44.03 1007.29 89.46 465.86
24.66 63.73 1011.4 74.52 444.37
16.38 47.45 1010.08 88.86 450.69
13.91 39.35 1014.69 75.51 469.02
23.18 51.3 1012.04 78.64 448.86
22.47 47.45 1007.62 76.65 447.14
13.39 44.85 1017.24 80.44 469.18
9.28 41.54 1018.33 79.89 482.8
11.82 42.86 1014.12 88.28 476.7
10.27 40.64 1020.63 84.6 474.99
22.92 63.94 1019.28 42.69 444.22
16.0 37.87 1020.24 78.41 461.33
21.22 43.43 1010.96 61.07 448.06
13.46 44.71 1014.51 50.0 474.6
9.39 40.11 1029.14 77.29 473.05
31.07 73.5 1010.58 43.66 432.06
12.82 38.62 1018.71 83.8 467.41
32.57 78.92 1011.6 66.47 430.12
8.11 42.18 1014.82 93.09 473.62
13.92 39.39 1012.94 80.52 471.81
23.04 59.43 1010.23 68.99 442.99
27.31 64.44 1014.65 57.27 442.77
5.91 39.33 1010.18 95.53 491.49
25.26 61.08 1013.68 71.72 447.46
27.97 58.84 1002.25 57.88 446.11
26.08 52.3 1007.03 63.34 442.44
29.01 65.71 1013.61 48.07 446.22
12.18 40.1 1016.67 91.87 471.49
13.76 45.87 1008.89 87.27 463.5
25.5 58.79 1016.02 64.4 440.01
28.26 65.34 1014.56 43.4 441.03
21.39 62.96 1019.49 72.24 452.68
7.26 40.69 1020.43 90.22 474.91
10.54 34.03 1018.71 74.0 478.77
27.71 74.34 998.14 71.85 434.2
23.11 68.3 1017.83 86.62 437.91
7.51 41.01 1024.61 97.41 477.61
26.46 74.67 1016.65 84.44 431.65
29.34 74.34 998.58 81.55 430.57
10.32 42.28 1008.82 75.66 481.09
22.74 61.02 1009.56 79.41 445.56
13.48 39.85 1012.71 58.91 475.74
25.52 69.75 1010.36 90.06 435.12
21.58 67.25 1017.39 79.0 446.15
27.66 76.86 1001.31 69.47 436.64
26.96 69.45 1013.89 51.47 436.69
12.29 42.18 1016.53 83.13 468.75
15.86 43.02 1012.18 40.33 466.6
13.87 45.08 1024.42 81.69 465.48
24.09 73.68 1014.93 94.55 441.34
20.45 69.45 1012.53 91.81 441.83
15.07 39.3 1019.0 63.62 464.7
32.72 69.75 1009.6 49.35 437.99
18.23 58.96 1015.55 69.61 459.12
35.56 68.94 1006.56 38.75 429.69
18.36 51.43 1010.57 90.17 459.8
26.35 64.05 1009.81 81.24 433.63
25.92 60.95 1014.62 48.46 442.84
8.01 41.66 1014.49 76.72 485.13
19.63 52.72 1025.09 51.16 459.12
20.02 67.32 1012.05 76.34 445.31
10.08 40.72 1022.7 67.3 480.8
27.23 66.48 1005.23 52.38 432.55
23.37 63.77 1013.42 76.44 443.86
18.74 59.21 1018.3 91.55 449.77
14.81 43.69 1017.19 71.9 470.71
23.1 51.3 1011.93 80.05 452.17
10.72 41.38 1021.6 63.77 478.29
29.46 71.94 1006.96 62.26 428.54
8.1 40.64 1020.66 89.04 478.27
27.29 62.66 1007.63 58.02 439.58
17.1 49.69 1005.53 81.82 457.32
11.49 44.2 1018.79 91.14 475.51
23.69 65.59 1010.85 88.92 439.66
13.51 40.89 1011.03 84.83 471.99
9.64 39.35 1015.1 91.76 479.81
25.65 78.92 1010.83 86.56 434.78
21.59 61.87 1011.18 57.21 446.58
27.98 58.33 1013.92 54.25 437.76
18.8 39.72 1001.24 63.8 459.36
18.28 44.71 1016.99 33.71 462.28
13.55 43.48 1016.08 67.25 464.33
22.99 46.21 1010.71 60.11 444.36
23.94 59.39 1014.32 74.55 438.64
13.74 34.03 1018.69 67.34 470.49
21.3 41.1 1001.86 42.75 455.13
27.54 66.93 1017.06 55.2 450.22
24.81 63.73 1009.34 83.61 440.43
4.97 42.85 1014.02 88.78 482.98
15.22 50.88 1014.19 100.12 460.44
23.88 54.2 1012.81 64.52 444.97
33.01 68.67 1005.2 51.41 433.94
25.98 73.18 1012.28 85.78 439.73
28.18 73.88 1005.89 75.41 434.48
21.67 60.84 1017.93 81.63 442.33
17.67 45.09 1014.26 51.92 457.67
21.37 57.76 1018.8 70.12 454.66
28.69 67.25 1017.71 53.83 432.21
16.61 43.77 1012.25 77.23 457.66
27.91 63.76 1010.27 65.67 435.21
20.97 47.43 1007.64 71.18 448.22
10.8 41.66 1013.79 81.96 475.51
20.61 62.91 1013.24 79.54 446.53
25.45 57.32 1011.7 47.09 441.3
30.16 69.34 1007.67 57.69 433.54
4.99 39.04 1020.45 78.89 472.52
10.51 44.78 1012.59 85.29 474.77
33.79 69.05 1001.62 40.13 435.1
21.34 59.8 1016.92 77.06 450.74
23.4 65.06 1014.32 67.38 442.7
32.21 68.14 1003.34 62.44 426.56
14.26 42.32 1016.0 77.43 463.71
27.71 66.93 1016.85 58.77 447.06
21.95 57.76 1018.02 67.72 452.27
25.76 63.94 1018.49 42.14 445.78
23.68 68.3 1017.93 84.16 438.65
8.28 40.77 1011.55 89.79 480.15
23.44 62.52 1016.46 67.21 447.19
25.32 48.41 1008.47 72.14 443.04
3.94 39.9 1008.06 97.49 488.81
17.3 57.76 1016.26 87.74 455.75
18.2 49.39 1018.83 96.3 455.86
21.43 46.97 1013.94 61.25 457.68
11.16 40.05 1014.95 88.38 479.11
30.38 74.16 1007.44 74.77 432.84
23.36 62.52 1016.18 68.18 448.37
21.69 47.45 1007.56 77.2 447.06
23.62 49.21 1014.1 49.54 443.53
21.87 61.45 1011.13 92.22 445.21
29.25 66.51 1015.53 33.65 441.7
20.03 66.86 1013.05 64.59 450.93
18.14 49.78 1002.95 100.09 451.44
24.23 56.89 1012.32 68.04 441.29
18.11 44.85 1014.48 48.94 458.85
6.57 43.65 1018.24 74.47 481.46
12.56 43.41 1016.93 81.02 467.19
13.4 41.58 1020.5 71.17 461.54
27.1 52.84 1006.28 53.85 439.08
14.28 42.74 1028.79 70.67 467.22
16.29 44.34 1019.49 59.36 468.8
31.24 71.98 1004.66 57.17 426.93
10.57 37.73 1024.36 70.29 474.65
13.8 44.21 1022.93 83.37 468.97
25.3 71.58 1010.18 87.36 433.97
18.06 50.16 1009.52 100.09 450.53
25.42 59.04 1011.98 68.78 444.51
15.07 40.69 1015.29 70.98 469.03
11.75 71.14 1019.36 75.68 466.56
20.23 52.05 1012.15 47.49 457.57
27.31 59.54 1006.24 71.99 440.13
28.57 69.84 1003.57 66.55 433.24
17.9 43.72 1008.64 74.73 452.55
23.83 71.37 1002.04 64.78 443.29
27.92 74.99 1005.47 75.13 431.76
17.34 44.78 1007.81 56.38 454.97
17.94 63.07 1012.42 94.35 456.7
6.4 39.9 1007.75 86.55 486.03
11.78 39.96 1011.37 82.95 472.79
20.28 57.25 1010.12 88.42 452.03
21.04 54.2 1012.26 85.61 443.41
25.11 67.32 1014.49 58.39 441.93
30.28 70.98 1007.51 74.28 432.64
8.14 36.24 1013.15 87.85 480.25
16.86 39.63 1004.47 83.5 466.68
6.25 40.07 1020.19 65.24 494.39
22.35 54.42 1012.46 75.01 454.72
17.98 56.85 1012.28 84.52 448.71
21.19 42.48 1013.43 80.52 469.76
20.94 44.89 1009.64 75.14 450.71
24.23 58.79 1009.8 75.75 444.01
19.18 58.2 1017.46 76.72 453.2
20.88 57.85 1012.39 85.47 450.87
23.67 63.86 1019.67 57.95 441.73
14.12 39.52 1018.41 78.32 465.09
25.23 64.63 1020.59 52.2 447.28
6.54 39.33 1011.54 93.69 491.16
20.08 62.52 1017.99 75.74 450.98
24.67 63.56 1013.75 67.56 446.3
27.82 79.74 1008.37 69.46 436.48
15.55 42.03 1017.41 74.58 460.84
24.26 69.51 1013.43 53.23 442.56
13.45 41.49 1020.19 88.72 467.3
11.06 40.64 1021.47 96.16 479.13
24.91 52.3 1008.72 68.26 441.15
22.39 59.04 1011.78 86.39 445.52
11.95 40.69 1015.62 85.34 475.4
14.85 40.69 1014.91 72.64 469.3
10.11 41.62 1017.17 97.82 463.57
23.67 68.67 1006.71 77.22 445.32
16.14 44.21 1020.36 80.59 461.03
15.11 43.13 1014.99 46.91 466.74
24.14 59.87 1018.47 57.76 444.04
30.08 67.25 1017.6 53.09 434.01
14.77 44.9 1020.5 84.31 465.23
27.6 69.34 1009.63 71.58 440.6
13.89 44.84 1023.66 92.97 466.74
26.85 75.6 1017.43 74.55 433.48
12.41 40.96 1023.36 78.96 473.59
13.08 41.74 1020.75 64.44 474.81
18.93 44.06 1017.58 68.23 454.75
20.5 49.69 1009.6 70.81 452.94
30.72 69.13 1009.94 61.66 435.83
7.55 39.22 1014.53 77.76 482.19
13.49 44.47 1030.46 69.49 466.66
15.62 40.12 1013.03 96.26 462.59
24.8 64.63 1020.69 55.74 447.82
10.03 41.62 1014.55 95.61 462.73
22.43 63.21 1012.06 84.75 447.98
14.95 39.31 1009.15 75.3 462.72
24.78 58.46 1016.82 67.5 442.42
23.2 48.41 1008.64 80.92 444.69
14.01 39.0 1016.73 79.23 466.7
19.4 64.63 1020.38 81.1 453.84
30.15 67.32 1013.83 32.8 436.92
6.91 36.08 1021.82 84.31 486.37
29.04 60.07 1015.42 46.15 440.43
26.02 63.07 1010.94 53.96 446.82
5.89 39.48 1005.11 59.83 484.91
26.52 71.64 1008.27 75.3 437.76
28.53 68.08 1013.27 42.53 438.91
16.59 39.54 1007.97 70.58 464.19
22.95 67.79 1009.89 91.69 442.19
23.96 47.43 1008.38 63.55 446.86
17.48 44.2 1018.89 61.51 457.15
6.69 43.65 1020.14 69.55 482.57
10.25 41.26 1007.44 98.08 476.03
28.87 72.58 1008.69 79.34 428.89
12.04 40.23 1018.07 81.28 472.7
22.58 52.3 1009.04 78.99 445.6
15.12 52.05 1014.63 80.38 464.78
25.48 58.95 1017.02 51.16 440.42
27.87 70.79 1003.96 72.17 428.41
23.72 70.47 1010.65 75.39 438.5
25.0 59.43 1007.84 68.91 438.28
8.42 40.64 1022.35 96.38 476.29
22.46 58.49 1011.5 70.54 448.46
29.92 57.19 1008.62 45.8 438.99
11.68 39.22 1017.9 57.95 471.8
14.04 42.44 1012.74 81.89 471.81
19.86 59.14 1016.12 69.32 449.82
25.99 68.08 1013.13 59.14 442.14
23.42 58.79 1009.74 81.54 441.46
10.6 40.22 1011.37 85.81 477.62
20.97 61.87 1011.45 65.41 446.76
14.14 39.82 1012.46 81.15 472.52
8.56 40.71 1021.27 95.87 471.58
24.86 72.39 1001.15 90.24 440.85
29.0 77.54 1011.33 75.13 431.37
27.59 71.97 1008.64 88.22 437.33
10.45 40.71 1015.68 81.48 469.22
8.51 40.78 1023.51 89.84 471.11
29.82 66.51 1010.98 43.57 439.17
22.56 62.26 1012.11 63.16 445.33
11.38 39.22 1018.62 57.14 473.71
20.25 57.76 1016.28 77.76 452.66
22.42 59.43 1007.12 90.56 440.99
14.85 38.91 1014.48 60.98 467.42
25.62 58.82 1010.02 70.31 444.14
19.85 56.53 1020.57 74.05 457.17
13.67 54.3 1015.92 75.42 467.87
24.39 70.72 1009.78 82.25 442.04
16.07 44.58 1019.52 67.95 471.36
11.6 39.1 1009.81 100.09 460.7
31.38 70.83 1010.35 47.28 431.33
29.91 76.86 998.59 72.41 432.6
19.67 59.39 1014.07 77.67 447.61
27.18 64.79 1016.27 63.7 443.87
21.39 52.3 1009.2 79.77 446.87
10.45 41.01 1020.57 93.84 465.74
19.46 56.89 1014.02 84.95 447.86
23.55 62.96 1020.16 70.16 447.65
23.35 63.47 1011.78 84.24 437.87
9.26 41.66 1016.87 73.32 483.51
10.3 41.46 1018.21 86.17 479.65
20.94 58.16 1016.88 65.43 455.16
23.13 71.25 1002.49 94.59 431.91
12.77 41.5 1014.13 86.8 470.68
28.29 69.13 1009.29 58.18 429.28
19.13 59.21 1018.32 89.66 450.81
24.44 73.5 1011.49 87.39 437.73
20.32 44.6 1015.16 36.35 460.21
20.54 69.05 1001.6 79.62 442.86
12.16 45.0 1021.51 50.52 482.99
28.09 65.27 1013.27 51.96 440.0
9.25 41.82 1033.25 74.73 478.48
21.75 49.82 1015.01 78.33 455.28
23.7 66.56 1002.07 85.19 436.94
16.22 37.87 1022.36 83.13 461.06
24.75 69.45 1013.97 53.49 438.28
10.48 39.58 1011.81 88.86 472.61
29.53 70.79 1003.7 60.89 426.85
12.59 39.72 1017.76 61.14 470.18
23.5 54.42 1012.31 68.29 455.38
29.01 66.56 1006.44 57.62 428.32
9.75 42.49 1010.57 83.63 480.35
19.55 56.53 1020.2 78.1 455.56
21.05 58.33 1013.14 66.34 447.66
24.72 68.67 1006.74 79.02 443.06
21.19 58.86 1014.19 68.96 452.43
10.77 41.54 1019.94 71.13 477.81
28.68 73.77 1004.72 87.01 431.66
29.87 73.91 1004.53 74.3 431.8
22.99 68.67 1006.65 77.62 446.67
24.66 60.29 1018.0 59.56 445.26
32.63 69.89 1013.85 41.66 425.72
31.38 72.29 1008.73 73.27 430.58
23.87 60.27 1018.94 77.16 439.86
25.6 59.15 1013.31 67.02 441.11
27.62 71.14 1011.6 52.8 434.72
30.1 67.45 1014.23 39.04 434.01
12.19 41.17 1019.43 65.47 475.64
13.11 41.58 1020.43 74.32 460.44
28.29 68.67 1005.46 69.22 436.4
13.45 40.73 1018.7 93.88 461.03
10.98 41.54 1019.94 69.83 479.08
26.48 69.14 1009.31 84.11 435.76
13.07 45.51 1015.22 78.65 460.14
25.56 75.6 1017.37 69.31 442.2
22.68 50.78 1008.83 70.3 447.69
28.86 73.67 1006.65 68.23 431.15
22.7 63.56 1014.32 71.76 445.0
27.89 73.21 1001.32 85.88 431.59
13.78 44.47 1027.94 71.09 467.22
28.14 51.43 1012.16 52.67 445.33
11.8 45.09 1013.21 89.68 470.57
10.71 39.61 1018.72 73.66 473.77
24.54 60.29 1017.42 58.94 447.67
11.54 40.05 1014.78 87.05 474.29
29.47 71.32 1008.07 67.0 437.14
29.24 69.05 1003.12 43.18 432.56
14.51 41.79 1009.72 80.62 459.14
22.91 60.07 1016.03 59.72 446.19
27.02 71.77 1006.38 72.1 428.1
13.49 44.47 1030.18 69.15 468.46
30.24 66.75 1017.95 55.66 435.02
23.19 48.6 1002.38 61.19 445.52
17.73 40.55 1003.36 74.62 462.69
18.62 61.27 1019.26 73.35 455.75
12.85 40.0 1015.89 68.85 463.74
32.33 69.68 1011.95 39.89 439.79
25.09 58.95 1016.99 53.16 443.26
29.45 69.13 1009.3 52.97 432.04
16.91 43.96 1013.32 79.87 465.86
14.09 45.87 1009.05 84.09 465.6
10.73 25.36 1009.35 100.15 469.43
23.2 49.3 1003.4 79.77 440.75
8.21 38.91 1015.82 88.99 481.32
9.3 40.56 1022.64 76.14 479.87
16.97 39.16 1005.7 69.13 458.59
23.69 71.97 1009.62 93.03 438.62
25.13 59.44 1012.38 77.92 445.59
9.86 43.56 1015.13 74.89 481.87
11.33 41.5 1013.58 88.7 475.01
26.95 48.41 1008.53 62.94 436.54
15.0 40.66 1016.28 89.62 456.63
20.76 62.52 1015.63 81.04 451.69
14.29 39.59 1010.93 94.53 463.04
19.74 67.71 1007.68 64.02 446.1
26.68 59.92 1009.94 70.57 438.67
14.24 41.4 1019.7 70.32 466.88
21.98 48.41 1008.42 84.86 444.6
22.75 59.39 1015.4 81.41 440.26
8.34 40.96 1023.28 89.45 483.92
11.8 41.2 1017.18 82.71 475.19
8.81 44.68 1023.06 93.93 479.24
30.05 73.68 1014.95 70.6 434.92
16.01 65.46 1014.0 87.68 454.16
21.75 58.79 1012.42 87.58 447.58
13.94 41.26 1021.67 74.4 467.9
29.25 69.13 1010.27 67.35 426.29
22.33 45.87 1007.8 63.61 447.02
16.43 41.79 1005.47 76.89 455.85
11.5 40.22 1010.31 78.08 476.46
23.53 68.94 1007.53 69.17 437.48
21.86 49.21 1014.61 53.31 452.77
6.17 39.33 1012.57 93.32 491.54
30.19 64.79 1017.22 42.47 438.41
11.67 41.93 1019.81 82.58 476.1
15.34 36.99 1007.87 94.59 464.58
11.5 40.78 1023.91 86.31 467.74
25.53 57.17 1010.0 72.57 442.12
21.27 57.5 1014.53 80.76 453.34
28.37 69.13 1010.44 71.93 425.29
28.39 51.43 1011.74 47.54 449.63
13.78 45.78 1025.27 95.72 462.88
14.6 42.32 1015.71 77.03 464.67
5.1 35.57 1027.17 80.49 489.96
7.0 38.08 1020.27 77.67 482.38
26.3 77.95 1009.45 78.72 437.95
30.56 71.98 1004.74 58.77 429.2
21.09 46.63 1013.03 74.8 453.34
28.21 70.02 1010.58 51.34 442.47
15.84 49.69 1015.14 90.41 462.6
10.03 40.96 1024.57 91.1 478.79
20.37 52.05 1012.34 62.57 456.11
21.19 50.16 1005.81 84.27 450.33
33.73 69.88 1007.21 42.93 434.83
29.87 73.68 1015.1 40.96 433.43
19.62 62.96 1020.76 76.53 456.02
9.93 40.67 1018.08 69.74 485.23
9.43 37.14 1013.03 74.99 473.57
14.24 39.58 1011.17 70.45 469.94
12.97 49.83 1008.69 91.49 452.07
7.6 41.04 1021.82 88.97 475.32
8.39 36.24 1013.39 89.13 480.69
25.41 48.06 1013.12 46.52 444.01
18.43 56.03 1020.41 60.55 465.17
10.31 39.82 1012.87 88.71 480.61
11.29 41.5 1013.39 89.15 476.04
22.61 49.3 1003.51 83.02 441.76
29.34 71.98 1005.19 75.19 428.24
18.87 67.71 1004.0 87.35 444.77
13.21 45.87 1008.58 85.66 463.1
11.3 44.6 1018.19 91.66 470.5
29.23 72.99 1007.04 63.47 431.0
27.76 69.4 1004.27 72.25 430.68
29.26 67.17 1006.6 70.58 436.42
25.72 49.82 1016.19 60.1 452.33
23.43 63.94 1010.64 89.29 440.16
25.6 63.76 1010.18 67.43 435.75
22.3 44.57 1008.48 67.58 449.74
27.91 72.24 1010.74 70.8 430.73
30.35 77.17 1009.55 63.62 432.75
21.78 47.43 1007.88 66.68 446.79
7.19 41.39 1018.12 90.76 486.35
20.88 59.8 1015.66 75.34 453.18
24.19 50.23 1015.73 59.77 458.31
9.98 41.54 1019.7 80.79 480.26
23.47 51.3 1011.89 74.1 448.65
26.35 49.5 1012.67 41.34 458.41
29.89 64.69 1006.37 58.78 435.39
19.29 50.16 1010.49 97.78 450.21
17.48 43.14 1018.68 74.85 459.59
25.21 75.6 1017.19 69.84 445.84
23.3 48.78 1018.17 75.36 441.08
15.42 37.85 1009.89 85.8 467.33
21.44 63.09 1016.56 90.11 444.19
29.45 68.27 1007.96 61.63 432.96
29.69 47.93 1002.85 44.76 438.09
15.52 36.99 1006.86 89.7 467.9
11.47 43.67 1012.68 72.51 475.72
9.77 34.69 1027.72 74.98 477.51
22.6 69.84 1006.37 79.59 435.13
8.24 39.61 1017.99 78.42 477.9
17.01 44.2 1019.18 61.23 457.26
19.64 44.6 1015.88 47.56 467.53
10.61 41.58 1021.08 93.06 465.15
12.04 40.1 1014.42 89.65 474.28
29.19 65.71 1013.85 50.5 444.49
21.75 45.09 1014.15 44.84 452.84
23.66 77.54 1008.5 85.32 435.38
27.05 75.33 1003.88 82.94 433.57
29.63 69.71 1009.04 67.26 435.27
18.2 39.63 1005.35 79.05 468.49
32.22 70.8 1009.9 62.03 433.07
26.88 73.56 1004.85 94.36 430.63
29.05 65.74 1013.29 60.02 440.74
8.9 39.96 1026.31 95.46 474.49
18.93 48.6 1005.72 84.92 449.74
27.49 63.76 1010.09 62.8 436.73
23.1 70.79 1006.53 90.81 434.58
11.22 43.13 1017.24 80.9 473.93
31.97 79.74 1007.03 55.84 435.99
13.32 43.22 1009.45 75.3 466.83
31.68 68.24 1005.29 37.34 427.22
23.69 63.77 1013.39 79.5 444.07
13.83 41.49 1020.11 87.29 469.57
18.32 66.51 1015.18 81.5 459.89
11.05 40.71 1024.91 76.42 479.59
22.03 64.69 1007.21 75.75 440.92
10.23 41.46 1020.45 84.95 480.87
23.92 66.54 1009.93 62.37 441.9
29.38 69.68 1011.35 49.25 430.2
17.35 42.86 1014.62 74.16 465.16
9.81 44.45 1021.19 90.55 471.32
4.97 40.64 1020.91 94.28 485.43
5.15 40.07 1012.27 63.31 495.35
21.54 58.49 1010.85 78.9 449.12
7.94 42.02 1006.22 90.97 480.53
18.77 50.66 1014.89 87.34 457.07
21.69 69.94 1010.7 80.8 443.67
10.07 44.68 1023.44 90.95 477.52
13.83 39.64 1012.52 69.97 472.95
10.45 39.69 1003.92 89.45 472.54
11.56 40.71 1015.85 76.08 469.17
23.64 70.04 1011.09 83.35 435.21
10.48 40.22 1004.81 92.16 477.78
13.09 39.85 1012.86 58.42 475.89
10.67 40.23 1017.75 85.06 483.9
12.57 39.16 1016.53 88.91 476.2
14.45 43.34 1015.47 83.33 462.16
14.22 37.85 1011.24 88.49 471.05
6.97 41.26 1010.6 96.88 484.71
20.61 63.86 1015.43 73.86 446.34
14.67 42.28 1007.21 65.17 469.02
29.06 72.86 1004.23 69.41 432.12
14.38 40.1 1015.51 81.23 467.28
32.51 69.98 1013.29 54.07 429.66
11.79 45.09 1013.16 89.17 469.49
8.65 40.56 1023.23 78.85 485.87
9.75 40.81 1026.0 84.44 481.95
9.11 40.02 1031.1 83.02 479.03
23.39 69.13 1010.99 90.66 434.5
14.3 54.3 1015.16 75.29 464.9
17.49 63.94 1020.02 82.6 452.71
31.1 69.51 1010.84 45.4 429.74
19.77 56.65 1020.67 66.33 457.09
28.61 72.29 1011.61 45.33 446.77
13.52 41.48 1014.46 67.12 460.76
13.52 40.83 1008.31 84.14 471.95
17.57 46.21 1014.09 80.81 453.29
28.18 60.07 1016.34 49.13 441.61
14.29 46.18 1017.01 87.29 464.73
18.12 43.69 1016.91 52.95 464.68
31.27 73.91 1003.72 68.92 430.59
26.24 77.95 1014.19 85.21 438.01
7.44 41.04 1021.84 88.56 479.08
29.78 74.78 1009.28 55.09 436.39
23.37 65.46 1016.25 48.64 447.07
10.62 39.58 1011.9 87.85 479.91
5.84 43.02 1013.88 87.42 489.05
14.51 53.82 1016.46 62.75 463.17
11.31 42.02 1001.18 94.86 471.26
11.25 40.67 1011.64 63.54 480.49
9.18 39.42 1025.41 69.46 473.78
19.82 58.16 1016.76 74.66 455.5
24.77 58.41 1013.78 80.57 446.27
9.66 41.06 1021.21 84.7 482.2
21.96 59.8 1016.72 72.6 452.48
18.59 43.14 1011.92 52.63 464.48
24.75 69.89 1015.29 82.01 438.1
24.37 63.47 1012.77 75.22 445.6
29.6 67.79 1010.37 51.05 442.43
25.32 61.25 1011.56 80.1 436.67
16.15 41.85 1016.54 81.58 466.56
15.74 71.14 1019.65 65.94 457.29
5.97 36.25 1029.65 86.74 487.03
15.84 52.72 1026.45 62.57 464.93
14.84 44.63 1019.28 57.37 466.0
12.25 48.79 1017.44 88.91 469.52
27.38 70.04 1011.18 72.26 428.88
8.76 41.48 1018.49 74.98 474.3
15.54 39.31 1009.69 71.19 461.06
18.71 39.39 1014.09 62.82 465.57
13.06 41.78 1012.3 55.31 467.67
12.72 40.71 1016.02 71.57 466.99
19.83 39.39 1013.73 59.16 463.72
27.23 49.16 1004.03 40.8 443.78
24.27 68.28 1005.43 67.63 445.23
11.8 40.66 1017.13 97.2 464.43
6.76 36.25 1028.31 91.16 484.36
25.99 63.07 1012.5 64.81 442.16
16.3 39.63 1004.64 85.61 464.11
16.5 49.39 1018.35 93.42 462.48
10.59 42.49 1009.59 77.36 477.49
26.05 65.59 1012.78 67.03 437.04
19.5 40.79 1003.8 89.45 457.09
22.21 45.01 1012.22 54.84 450.6
17.86 45.0 1023.25 53.48 465.78
29.96 70.04 1010.15 54.47 427.1
19.08 44.63 1020.14 43.36 459.81
23.59 47.43 1006.64 48.92 447.36
3.38 39.64 1011.0 81.22 488.92
26.39 66.49 1012.96 60.35 433.36
8.99 39.04 1021.99 75.98 483.35
10.91 41.04 1026.57 74.24 469.53
13.08 39.82 1012.27 85.21 476.96
23.95 58.46 1017.5 68.46 440.75
15.64 43.71 1024.51 78.31 462.55
18.78 54.2 1012.05 89.25 448.04
20.65 50.59 1016.22 68.57 455.24
4.96 40.07 1011.8 67.38 494.75
23.51 57.32 1012.55 53.6 444.58
5.99 35.79 1011.56 91.69 484.82
23.65 66.05 1019.6 78.21 442.9
5.17 39.33 1009.68 94.19 485.46
26.38 49.5 1012.82 37.19 457.81
6.02 43.65 1013.85 83.53 481.92
23.2 61.02 1009.63 79.45 443.23
8.57 39.69 1000.91 99.9 474.29
30.72 71.58 1009.98 50.39 430.46
21.52 50.66 1013.56 74.33 455.71
22.93 62.26 1011.25 83.66 438.34
5.71 41.31 1003.24 89.48 485.83
18.62 44.06 1017.76 64.59 452.82
27.88 68.94 1007.68 75.68 435.04
22.32 59.8 1016.82 64.18 451.21
14.55 42.74 1028.41 70.09 465.81
17.83 44.92 1025.04 70.58 458.42
9.68 39.96 1026.09 99.28 470.22
19.41 49.39 1020.84 81.89 449.24
13.22 44.92 1023.84 87.99 471.43
12.24 44.92 1023.74 88.21 473.26
19.21 58.49 1011.7 91.29 452.82
29.74 70.32 1008.1 52.72 432.69
23.28 60.84 1017.91 67.5 444.13
8.02 41.92 1029.8 92.05 467.21
22.47 48.6 1002.33 63.23 445.98
27.51 73.77 1002.42 90.88 436.91
17.51 44.9 1009.05 74.91 455.01
23.22 66.56 1002.47 85.39 437.11
11.73 40.64 1020.68 96.98 477.06
21.19 67.71 1006.65 56.28 441.71
5.48 40.07 1019.63 65.62 495.76
24.26 66.44 1011.33 55.32 445.63
12.32 41.62 1012.88 88.88 464.72
31.26 68.94 1005.94 39.49 438.03
32.09 72.86 1003.47 54.59 434.78
24.98 60.32 1015.63 57.19 444.67
27.48 61.41 1012.2 45.06 452.24
21.04 45.09 1014.19 40.62 450.92
27.75 70.4 1006.65 90.21 436.53
22.79 71.77 1005.75 90.91 435.53
24.22 68.51 1013.23 74.96 440.01
27.06 64.45 1008.72 54.21 443.1
29.25 71.94 1007.18 63.62 427.49
26.86 68.08 1012.99 50.04 436.25
29.64 67.79 1009.99 51.23 440.74
19.92 63.31 1015.02 82.71 443.54
18.5 51.43 1010.82 92.04 459.42
23.71 60.23 1009.76 90.67 439.66
14.39 44.84 1023.55 91.14 464.15
19.3 56.65 1020.55 70.43 459.1
24.65 52.36 1014.76 66.63 455.68
13.5 45.51 1015.33 86.95 469.08
9.82 41.26 1007.71 96.69 478.02
18.4 44.06 1017.36 70.88 456.8
28.12 44.89 1009.18 47.14 441.13
17.15 43.69 1017.05 63.36 463.88
30.69 73.67 1006.14 60.58 430.45
28.82 65.71 1014.24 54.3 449.18
21.3 48.92 1010.92 65.09 447.89
30.58 70.04 1010.4 48.16 431.59
21.17 52.3 1009.36 81.51 447.5
9.87 41.82 1033.04 68.57 475.58
22.18 59.8 1016.77 73.16 453.24
24.39 63.21 1012.59 80.88 446.4
10.73 44.92 1025.1 85.4 476.81
9.38 40.46 1019.29 75.77 474.1
20.27 57.76 1016.66 75.76 450.71
24.82 66.48 1006.4 70.21 433.62
16.55 41.66 1011.45 55.53 465.14
20.73 59.87 1019.08 80.48 445.18
9.51 39.22 1015.3 72.41 474.12
8.63 43.79 1016.08 83.25 483.91
6.48 40.27 1010.55 82.12 486.68
14.95 43.52 1022.43 94.75 464.98
5.76 45.87 1010.83 95.79 481.4
10.94 39.04 1021.81 86.02 479.2
15.87 41.16 1005.85 78.29 463.86
12.42 38.25 1012.76 82.23 472.3
29.12 58.84 1001.31 52.86 446.51
29.12 51.43 1005.93 60.66 437.71
19.08 41.1 1001.96 62.77 458.94
31.06 67.17 1007.62 65.54 437.91
5.72 39.33 1009.96 95.4 490.76
26.52 65.06 1013.4 51.78 439.66
13.84 44.9 1007.58 63.62 463.27
13.03 39.52 1016.68 83.09 473.99
25.94 66.49 1012.83 61.81 433.38
16.64 53.82 1015.13 68.24 459.01
14.13 40.75 1016.05 72.41 471.44
13.65 39.28 1012.97 79.64 471.91
14.5 44.47 1028.2 66.95 465.15
19.8 51.19 1008.25 91.98 446.66
25.2 63.76 1009.78 64.96 438.15
20.66 51.19 1008.81 88.93 447.14
12.07 43.71 1025.53 85.62 472.32
25.64 70.72 1010.16 84.0 441.68
23.33 72.99 1009.33 89.41 440.04
29.41 64.05 1009.82 67.4 444.82
16.6 53.16 1014.5 76.75 457.26
27.53 72.58 1009.13 89.06 428.83
20.62 43.43 1009.93 64.02 449.07
26.02 71.94 1009.38 64.12 435.21
12.75 44.2 1017.59 81.22 471.03
12.87 48.04 1012.47 100.13 465.56
25.77 62.96 1019.86 58.07 442.83
14.84 41.48 1017.26 63.42 460.3
7.41 40.71 1023.07 83.32 474.25
8.87 41.82 1033.3 74.28 477.97
9.69 40.46 1019.1 71.91 472.16
16.17 46.97 1014.22 85.8 456.08
26.24 49.82 1014.9 55.58 452.41
13.78 43.22 1011.31 69.7 463.71
26.3 67.07 1006.26 63.79 433.72
17.37 57.76 1016.0 86.59 456.4
23.6 48.98 1015.41 48.28 448.43
8.3 36.08 1020.63 80.42 481.6
18.86 42.18 1001.16 98.58 457.07
22.12 49.39 1019.8 72.83 451.0
28.41 75.6 1018.48 56.07 440.28
29.42 71.32 1002.26 67.13 437.47
18.61 67.71 1004.07 84.49 443.57
27.57 69.84 1004.91 68.37 426.6
12.83 41.5 1013.12 86.07 470.87
9.64 39.85 1012.9 83.82 478.37
19.13 58.66 1013.32 74.86 453.92
15.92 40.56 1020.79 53.52 470.22
24.64 72.24 1011.37 80.61 434.54
27.62 63.9 1013.11 43.56 442.89
8.9 36.24 1013.29 89.35 479.03
9.55 43.99 1020.5 97.28 476.06
10.57 36.71 1022.62 80.49 473.88
19.8 57.25 1010.84 88.9 451.75
25.63 56.85 1012.68 49.7 439.2
24.7 58.46 1015.58 68.64 439.7
15.26 46.18 1013.68 98.58 463.6
20.06 52.84 1004.21 82.12 447.47
19.84 56.89 1013.23 78.32 447.92
11.49 44.63 1020.44 86.04 471.08
23.74 72.43 1007.99 91.36 437.55
22.62 51.3 1012.36 81.02 448.27
29.53 72.39 998.47 76.05 431.69
21.32 48.14 1016.57 71.81 449.09
20.3 58.46 1015.93 82.13 448.79
16.97 44.92 1025.21 74.27 460.21
12.07 41.17 1013.54 71.32 479.28
7.46 41.82 1032.67 74.59 483.11
19.2 54.2 1011.46 84.44 450.75
28.64 66.54 1010.43 43.39 437.97
13.56 41.48 1008.53 87.2 459.76
17.4 44.9 1020.5 77.11 457.75
14.08 40.1 1015.48 82.81 469.33
27.11 69.75 1009.74 85.67 433.28
20.92 70.02 1010.23 95.58 444.64
16.18 44.9 1021.3 74.46 463.1
15.57 44.68 1022.01 90.02 460.91
10.37 39.04 1023.95 81.93 479.35
19.6 59.21 1017.65 86.29 449.23
9.22 40.92 1021.83 85.43 474.51
27.76 72.99 1007.81 71.66 435.02
28.68 70.72 1009.43 71.33 435.45
20.95 48.14 1013.3 67.72 452.38
9.06 39.3 1019.73 84.23 480.41
9.21 39.72 1019.54 74.44 478.96
13.65 42.74 1026.58 71.48 468.87
31.79 76.2 1007.89 56.3 434.01
14.32 44.6 1013.85 68.13 466.36
26.28 75.23 1011.44 68.35 435.28
7.69 43.02 1014.51 85.23 486.46
14.44 40.1 1015.51 79.78 468.19
9.19 41.01 1022.14 98.98 468.37
13.35 41.39 1019.17 72.87 474.19
23.04 74.22 1009.52 90.93 440.32
4.83 38.44 1015.35 72.94 485.32
17.29 42.86 1014.38 72.3 464.27
8.73 36.18 1013.66 77.74 479.25
26.21 70.32 1007.0 78.29 430.4
23.72 58.62 1016.65 69.1 447.49
29.27 64.69 1006.85 55.79 438.23
10.4 40.43 1025.46 75.09 492.09
12.19 40.75 1015.13 88.98 475.36
20.4 54.9 1016.68 64.26 452.56
34.3 74.67 1015.98 25.89 427.84
27.56 68.08 1010.8 59.18 433.95
30.9 70.8 1008.48 67.48 435.27
14.85 58.59 1014.04 89.85 454.62
16.42 40.56 1020.36 50.62 472.17
16.45 63.31 1015.96 83.97 452.42
10.14 42.02 1003.19 96.51 472.17
9.53 41.44 1018.01 80.09 481.83
17.01 49.15 1021.83 84.02 458.78
23.94 62.08 1022.47 61.97 447.5
15.95 49.25 1019.04 88.51 463.4
11.15 41.26 1022.67 81.83 473.57
25.56 70.32 1009.07 90.63 433.72
27.16 66.44 1011.2 73.37 431.85
26.71 77.95 1012.13 77.5 433.47
29.56 74.22 1007.45 57.46 432.84
31.19 70.94 1007.29 51.91 436.6
6.86 41.17 1020.12 79.14 490.23
12.36 41.74 1020.58 69.24 477.16
32.82 68.31 1010.44 41.85 441.06
25.3 70.98 1007.22 95.1 440.86
8.71 41.82 1033.08 74.53 477.94
13.34 40.8 1026.56 64.85 474.47
14.2 43.02 1012.18 57.07 470.67
23.74 65.34 1013.7 62.9 447.31
16.9 44.88 1018.14 72.21 466.8
28.54 71.94 1007.4 65.99 430.91
30.15 69.88 1007.2 73.67 434.75
14.33 42.86 1010.82 88.59 469.52
25.57 59.43 1008.88 61.19 438.9
30.55 70.04 1010.51 49.37 429.56
28.04 74.33 1013.53 48.65 432.92
26.39 49.16 1005.68 56.18 442.87
15.3 41.76 1022.57 71.56 466.59
6.03 41.14 1028.04 87.46 479.61
13.49 44.63 1019.12 70.02 471.08
27.67 59.14 1016.51 61.2 433.37
24.19 65.48 1018.8 60.54 443.92
24.44 59.14 1016.74 71.82 443.5
29.86 64.79 1017.37 44.8 439.89
30.2 69.59 1008.9 67.32 434.66
7.99 41.38 1021.95 78.77 487.57
9.93 41.62 1013.76 96.02 464.64
11.03 42.32 1017.26 90.56 470.92
22.34 63.73 1014.37 83.19 444.39
25.33 48.6 1002.54 68.45 442.48
18.87 52.08 1005.25 99.19 449.61
25.97 69.34 1009.43 88.11 435.02
16.58 43.99 1021.81 79.29 458.67
14.35 46.18 1016.63 87.76 461.74
25.06 62.39 1008.09 82.56 438.31
13.85 48.92 1011.68 79.24 462.38
16.09 44.2 1019.39 67.24 460.56
26.34 59.21 1013.37 58.98 439.22
23.01 58.79 1009.71 84.22 444.64
26.39 71.25 999.8 89.12 430.34
31.32 71.29 1008.37 50.07 430.46
16.64 45.87 1009.02 98.86 456.79
13.42 41.23 994.17 95.79 468.82
20.06 44.9 1008.79 70.06 448.51
14.8 44.71 1014.67 41.71 470.77
12.59 41.14 1025.79 86.55 465.74
26.7 66.56 1005.31 71.97 430.21
19.78 50.32 1008.62 96.4 449.23
15.17 49.15 1021.91 91.73 461.89
21.71 61.45 1010.97 91.62 445.72
19.09 39.39 1013.36 59.14 466.13
19.76 51.19 1008.38 92.56 448.71
14.68 41.23 998.43 83.71 469.25
21.3 66.86 1013.04 55.43 450.56
16.73 39.64 1008.94 74.91 464.46
12.26 41.5 1014.87 89.41 471.13
14.77 48.06 1010.92 69.81 461.52
18.26 59.15 1012.04 86.01 451.09
27.1 79.74 1005.43 86.05 431.51
14.72 40.83 1009.65 80.98 469.8
26.3 51.43 1012.05 63.62 442.28
16.48 48.92 1011.84 64.16 458.67
17.99 43.79 1016.13 75.63 462.4
20.34 59.8 1015.18 80.21 453.54
25.53 62.96 1019.81 59.7 444.38
31.59 58.9 1003.39 47.6 440.52
30.8 69.14 1007.68 63.78 433.62
10.75 45.0 1023.68 89.37 481.96
19.3 44.9 1008.89 70.55 452.75
4.71 39.42 1026.4 84.42 481.28
23.1 66.05 1020.28 80.62 439.03
32.63 73.88 1005.64 52.56 435.75
26.63 74.16 1009.72 83.26 436.03
24.35 58.49 1011.03 70.64 445.6
15.11 56.03 1020.27 89.95 462.65
29.1 50.05 1005.87 51.53 438.66
21.24 50.32 1008.54 84.83 447.32
6.16 39.48 1004.85 59.68 484.55
7.36 41.01 1024.9 97.88 476.8
10.44 39.04 1023.99 85.03 480.34
26.76 48.41 1010.53 47.38 440.63
16.79 44.6 1014.27 48.08 459.48
10.76 40.43 1025.98 79.65 490.78
6.07 38.91 1019.25 83.39 483.56
27.33 73.18 1012.26 82.18 429.38
27.15 59.21 1013.49 51.71 440.27
22.35 51.43 1011.34 77.33 445.34
21.82 65.27 1013.86 72.81 447.43
21.11 69.94 1004.37 84.26 439.91
19.95 50.59 1016.11 73.23 459.27
7.45 39.61 1017.88 79.73 478.89
15.36 41.66 1012.41 62.32 466.7
15.65 43.5 1021.39 78.58 463.5
25.31 74.33 1015.04 79.88 436.21
25.88 63.47 1011.95 65.87 443.94
24.6 63.94 1012.87 80.28 439.63
22.58 41.54 1013.21 71.33 460.95
19.69 59.14 1015.99 70.33 448.69
25.85 75.08 1006.24 57.73 444.63
10.06 37.83 1005.49 99.46 473.51
18.59 39.54 1008.56 68.61 462.56
18.27 50.16 1011.07 95.91 451.76
8.85 40.43 1025.68 80.42 491.81
30.04 68.08 1011.04 51.01 429.52
26.06 49.02 1007.59 74.08 437.9
14.8 38.73 1003.18 80.73 467.54
23.93 64.45 1015.35 54.71 449.97
23.72 66.48 1003.61 73.75 436.62
11.44 40.55 1023.37 88.43 477.68
20.28 63.86 1016.04 74.66 447.26
27.9 63.13 1011.8 70.04 439.76
24.74 59.39 1015.23 74.64 437.49
14.8 58.2 1018.29 85.11 455.14
8.22 41.03 1021.76 82.97 485.5
27.56 66.93 1016.81 55.59 444.1
32.07 70.94 1006.91 49.9 432.33
9.53 44.03 1008.87 89.99 471.23
13.61 42.34 1017.93 91.61 463.89
22.2 51.19 1009.2 82.95 445.54
21.36 59.54 1007.99 92.62 446.09
23.25 63.86 1017.82 59.64 445.12
23.5 59.21 1018.29 63.0 443.31
8.46 39.66 1015.14 85.38 484.16
8.19 40.69 1019.86 85.23 477.76
30.67 71.29 1008.36 52.08 430.28
32.48 62.04 1010.39 38.05 446.48
8.99 36.66 1028.11 71.98 481.03
13.77 47.83 1007.41 90.66 466.07
19.05 67.32 1013.2 83.14 447.47
21.19 55.5 1019.83 65.22 455.93
10.12 40.0 1021.15 91.67 479.62
24.93 47.01 1014.28 66.04 455.06
8.47 40.46 1019.87 78.19 475.06
24.52 56.85 1012.59 54.47 438.89
28.55 69.84 1003.38 67.26 432.7
20.58 50.9 1011.89 72.56 452.6
18.31 46.21 1010.46 82.15 451.75
27.18 71.06 1008.16 86.32 430.66
4.43 38.91 1019.04 88.17 491.9
26.02 74.78 1010.04 72.78 439.82
15.75 39.0 1015.91 69.58 460.73
22.99 60.95 1015.14 69.86 449.7
25.52 59.15 1013.88 65.37 439.42
27.04 65.06 1013.33 52.37 439.84
6.42 35.57 1025.58 79.63 485.86
17.04 40.12 1011.81 83.14 458.1
10.79 39.82 1012.89 88.25 479.92
20.41 56.03 1019.94 55.85 458.29
7.36 40.07 1017.29 52.55 489.45
28.08 73.42 1012.17 62.74 434.0
24.74 69.13 1010.69 90.08 431.24
28.32 47.93 1003.26 54.5 439.5
16.71 40.56 1019.48 49.88 467.46
30.7 71.58 1010.0 48.96 429.27
18.42 58.95 1016.95 86.77 452.1
10.62 42.02 999.83 96.66 472.41
22.18 69.05 1002.75 70.84 442.14
22.38 49.3 1003.56 83.83 441.0
13.94 41.58 1020.76 68.22 463.07
21.24 60.84 1017.99 82.22 445.71
6.76 39.81 1017.11 87.9 483.16
26.73 68.84 1010.75 66.83 440.45
7.24 38.06 1020.6 85.36 481.83
10.84 40.62 1015.53 60.9 467.6
19.32 52.84 1004.29 83.51 450.88
29.0 69.13 1001.22 52.96 425.5
23.38 54.42 1013.95 73.02 451.87
31.17 69.51 1010.51 43.11 428.94
26.17 48.6 1002.59 61.41 439.86
30.9 73.42 1011.21 65.32 433.44
24.92 73.68 1015.12 93.68 438.23
32.77 71.32 1007.68 42.39 436.95
14.37 40.56 1021.67 68.18 470.19
8.36 40.22 1011.6 89.18 484.66
31.45 68.27 1007.56 64.79 430.81
31.6 73.17 1010.05 43.48 433.37
17.9 48.98 1014.17 80.4 453.02
20.35 50.9 1012.6 72.43 453.5
16.21 41.23 995.88 80.0 463.09
19.36 44.6 1016.25 45.65 464.56
21.04 65.46 1017.22 63.02 452.12
14.05 40.69 1015.66 74.39 470.9
23.48 64.15 1021.08 57.77 450.89
21.91 63.76 1009.85 76.8 445.04
24.42 63.07 1011.49 67.39 444.72
14.26 40.92 1022.07 73.96 460.38
21.38 58.33 1013.05 72.75 446.8
15.71 44.06 1018.34 71.69 465.05
5.78 40.62 1016.55 84.98 484.13
6.77 39.81 1017.01 87.68 488.27
23.84 49.21 1013.85 50.36 447.09
21.17 58.16 1017.16 68.11 452.02
19.94 58.96 1014.16 66.27 455.55
8.73 41.92 1029.41 89.72 480.99
16.39 41.67 1012.96 61.07 467.68
res12: Long = 9568
+--------+--------------------+-----------+
|database|           tableName|isTemporary|
+--------+--------------------+-----------+
| default|power_plant_predi...|      false|
| default|    sentimentlex_csv|      false|
| default|        simple_range|      false|
| default|  social_media_usage|      false|
| default|social_media_usag...|      false|
+--------+--------------------+-----------+
+------------------------------------------------------------+--------+-----------+---------+-----------+
|name                                                        |database|description|tableType|isTemporary|
+------------------------------------------------------------+--------+-----------+---------+-----------+
|power_plant_predictions                                     |default |null       |MANAGED  |false      |
|sentimentlex_csv                                            |default |null       |EXTERNAL |false      |
|simple_range                                                |default |null       |MANAGED  |false      |
|social_media_usage                                          |default |null       |MANAGED  |false      |
|social_media_usage_table_partitionedbyplatformbucketedbydate|default |null       |MANAGED  |false      |
+------------------------------------------------------------+--------+-----------+---------+-----------+
+-------+---------------------+-------------------------+
|name   |description          |locationUri              |
+-------+---------------------+-------------------------+
|default|Default Hive database|dbfs:/user/hive/warehouse|
+-------+---------------------+-------------------------+

Step 6: Data Modeling

Now let's model our data to predict what the power output will be given a set of sensor readings

Our first model will be based on simple linear regression since we saw some linear patterns in our data based on the scatter plots during the exploration stage.

+--------+--------------------+-----------+
|database|           tableName|isTemporary|
+--------+--------------------+-----------+
| default|power_plant_predi...|      false|
| default|    sentimentlex_csv|      false|
| default|        simple_range|      false|
| default|  social_media_usage|      false|
| default|social_media_usag...|      false|
|        |   power_plant_table|       true|
+--------+--------------------+-----------+
AT V AP RH PE
14.96 41.76 1024.07 73.17 463.26
25.18 62.96 1020.04 59.08 444.37
5.11 39.4 1012.16 92.14 488.56
20.86 57.32 1010.24 76.64 446.48
10.82 37.5 1009.23 96.62 473.9
26.27 59.44 1012.23 58.77 443.67
15.89 43.96 1014.02 75.24 467.35
9.48 44.71 1019.12 66.43 478.42
14.64 45.0 1021.78 41.25 475.98
11.74 43.56 1015.14 70.72 477.5
17.99 43.72 1008.64 75.04 453.02
20.14 46.93 1014.66 64.22 453.99
24.34 73.5 1011.31 84.15 440.29
25.71 58.59 1012.77 61.83 451.28
26.19 69.34 1009.48 87.59 433.99
21.42 43.79 1015.76 43.08 462.19
18.21 45.0 1022.86 48.84 467.54
11.04 41.74 1022.6 77.51 477.2
14.45 52.75 1023.97 63.59 459.85
13.97 38.47 1015.15 55.28 464.3
17.76 42.42 1009.09 66.26 468.27
5.41 40.07 1019.16 64.77 495.24
7.76 42.28 1008.52 83.31 483.8
27.23 63.9 1014.3 47.19 443.61
27.36 48.6 1003.18 54.93 436.06
27.47 70.72 1009.97 74.62 443.25
14.6 39.31 1011.11 72.52 464.16
7.91 39.96 1023.57 88.44 475.52
5.81 35.79 1012.14 92.28 484.41
30.53 65.18 1012.69 41.85 437.89
23.87 63.94 1019.02 44.28 445.11
26.09 58.41 1013.64 64.58 438.86
29.27 66.85 1011.11 63.25 440.98
27.38 74.16 1010.08 78.61 436.65
24.81 63.94 1018.76 44.51 444.26
12.75 44.03 1007.29 89.46 465.86
24.66 63.73 1011.4 74.52 444.37
16.38 47.45 1010.08 88.86 450.69
13.91 39.35 1014.69 75.51 469.02
23.18 51.3 1012.04 78.64 448.86
22.47 47.45 1007.62 76.65 447.14
13.39 44.85 1017.24 80.44 469.18
9.28 41.54 1018.33 79.89 482.8
11.82 42.86 1014.12 88.28 476.7
10.27 40.64 1020.63 84.6 474.99
22.92 63.94 1019.28 42.69 444.22
16.0 37.87 1020.24 78.41 461.33
21.22 43.43 1010.96 61.07 448.06
13.46 44.71 1014.51 50.0 474.6
9.39 40.11 1029.14 77.29 473.05
31.07 73.5 1010.58 43.66 432.06
12.82 38.62 1018.71 83.8 467.41
32.57 78.92 1011.6 66.47 430.12
8.11 42.18 1014.82 93.09 473.62
13.92 39.39 1012.94 80.52 471.81
23.04 59.43 1010.23 68.99 442.99
27.31 64.44 1014.65 57.27 442.77
5.91 39.33 1010.18 95.53 491.49
25.26 61.08 1013.68 71.72 447.46
27.97 58.84 1002.25 57.88 446.11
26.08 52.3 1007.03 63.34 442.44
29.01 65.71 1013.61 48.07 446.22
12.18 40.1 1016.67 91.87 471.49
13.76 45.87 1008.89 87.27 463.5
25.5 58.79 1016.02 64.4 440.01
28.26 65.34 1014.56 43.4 441.03
21.39 62.96 1019.49 72.24 452.68
7.26 40.69 1020.43 90.22 474.91
10.54 34.03 1018.71 74.0 478.77
27.71 74.34 998.14 71.85 434.2
23.11 68.3 1017.83 86.62 437.91
7.51 41.01 1024.61 97.41 477.61
26.46 74.67 1016.65 84.44 431.65
29.34 74.34 998.58 81.55 430.57
10.32 42.28 1008.82 75.66 481.09
22.74 61.02 1009.56 79.41 445.56
13.48 39.85 1012.71 58.91 475.74
25.52 69.75 1010.36 90.06 435.12
21.58 67.25 1017.39 79.0 446.15
27.66 76.86 1001.31 69.47 436.64
26.96 69.45 1013.89 51.47 436.69
12.29 42.18 1016.53 83.13 468.75
15.86 43.02 1012.18 40.33 466.6
13.87 45.08 1024.42 81.69 465.48
24.09 73.68 1014.93 94.55 441.34
20.45 69.45 1012.53 91.81 441.83
15.07 39.3 1019.0 63.62 464.7
32.72 69.75 1009.6 49.35 437.99
18.23 58.96 1015.55 69.61 459.12
35.56 68.94 1006.56 38.75 429.69
18.36 51.43 1010.57 90.17 459.8
26.35 64.05 1009.81 81.24 433.63
25.92 60.95 1014.62 48.46 442.84
8.01 41.66 1014.49 76.72 485.13
19.63 52.72 1025.09 51.16 459.12
20.02 67.32 1012.05 76.34 445.31
10.08 40.72 1022.7 67.3 480.8
27.23 66.48 1005.23 52.38 432.55
23.37 63.77 1013.42 76.44 443.86
18.74 59.21 1018.3 91.55 449.77
14.81 43.69 1017.19 71.9 470.71
23.1 51.3 1011.93 80.05 452.17
10.72 41.38 1021.6 63.77 478.29
29.46 71.94 1006.96 62.26 428.54
8.1 40.64 1020.66 89.04 478.27
27.29 62.66 1007.63 58.02 439.58
17.1 49.69 1005.53 81.82 457.32
11.49 44.2 1018.79 91.14 475.51
23.69 65.59 1010.85 88.92 439.66
13.51 40.89 1011.03 84.83 471.99
9.64 39.35 1015.1 91.76 479.81
25.65 78.92 1010.83 86.56 434.78
21.59 61.87 1011.18 57.21 446.58
27.98 58.33 1013.92 54.25 437.76
18.8 39.72 1001.24 63.8 459.36
18.28 44.71 1016.99 33.71 462.28
13.55 43.48 1016.08 67.25 464.33
22.99 46.21 1010.71 60.11 444.36
23.94 59.39 1014.32 74.55 438.64
13.74 34.03 1018.69 67.34 470.49
21.3 41.1 1001.86 42.75 455.13
27.54 66.93 1017.06 55.2 450.22
24.81 63.73 1009.34 83.61 440.43
4.97 42.85 1014.02 88.78 482.98
15.22 50.88 1014.19 100.12 460.44
23.88 54.2 1012.81 64.52 444.97
33.01 68.67 1005.2 51.41 433.94
25.98 73.18 1012.28 85.78 439.73
28.18 73.88 1005.89 75.41 434.48
21.67 60.84 1017.93 81.63 442.33
17.67 45.09 1014.26 51.92 457.67
21.37 57.76 1018.8 70.12 454.66
28.69 67.25 1017.71 53.83 432.21
16.61 43.77 1012.25 77.23 457.66
27.91 63.76 1010.27 65.67 435.21
20.97 47.43 1007.64 71.18 448.22
10.8 41.66 1013.79 81.96 475.51
20.61 62.91 1013.24 79.54 446.53
25.45 57.32 1011.7 47.09 441.3
30.16 69.34 1007.67 57.69 433.54
4.99 39.04 1020.45 78.89 472.52
10.51 44.78 1012.59 85.29 474.77
33.79 69.05 1001.62 40.13 435.1
21.34 59.8 1016.92 77.06 450.74
23.4 65.06 1014.32 67.38 442.7
32.21 68.14 1003.34 62.44 426.56
14.26 42.32 1016.0 77.43 463.71
27.71 66.93 1016.85 58.77 447.06
21.95 57.76 1018.02 67.72 452.27
25.76 63.94 1018.49 42.14 445.78
23.68 68.3 1017.93 84.16 438.65
8.28 40.77 1011.55 89.79 480.15
23.44 62.52 1016.46 67.21 447.19
25.32 48.41 1008.47 72.14 443.04
3.94 39.9 1008.06 97.49 488.81
17.3 57.76 1016.26 87.74 455.75
18.2 49.39 1018.83 96.3 455.86
21.43 46.97 1013.94 61.25 457.68
11.16 40.05 1014.95 88.38 479.11
30.38 74.16 1007.44 74.77 432.84
23.36 62.52 1016.18 68.18 448.37
21.69 47.45 1007.56 77.2 447.06
23.62 49.21 1014.1 49.54 443.53
21.87 61.45 1011.13 92.22 445.21
29.25 66.51 1015.53 33.65 441.7
20.03 66.86 1013.05 64.59 450.93
18.14 49.78 1002.95 100.09 451.44
24.23 56.89 1012.32 68.04 441.29
18.11 44.85 1014.48 48.94 458.85
6.57 43.65 1018.24 74.47 481.46
12.56 43.41 1016.93 81.02 467.19
13.4 41.58 1020.5 71.17 461.54
27.1 52.84 1006.28 53.85 439.08
14.28 42.74 1028.79 70.67 467.22
16.29 44.34 1019.49 59.36 468.8
31.24 71.98 1004.66 57.17 426.93
10.57 37.73 1024.36 70.29 474.65
13.8 44.21 1022.93 83.37 468.97
25.3 71.58 1010.18 87.36 433.97
18.06 50.16 1009.52 100.09 450.53
25.42 59.04 1011.98 68.78 444.51
15.07 40.69 1015.29 70.98 469.03
11.75 71.14 1019.36 75.68 466.56
20.23 52.05 1012.15 47.49 457.57
27.31 59.54 1006.24 71.99 440.13
28.57 69.84 1003.57 66.55 433.24
17.9 43.72 1008.64 74.73 452.55
23.83 71.37 1002.04 64.78 443.29
27.92 74.99 1005.47 75.13 431.76
17.34 44.78 1007.81 56.38 454.97
17.94 63.07 1012.42 94.35 456.7
6.4 39.9 1007.75 86.55 486.03
11.78 39.96 1011.37 82.95 472.79
20.28 57.25 1010.12 88.42 452.03
21.04 54.2 1012.26 85.61 443.41
25.11 67.32 1014.49 58.39 441.93
30.28 70.98 1007.51 74.28 432.64
8.14 36.24 1013.15 87.85 480.25
16.86 39.63 1004.47 83.5 466.68
6.25 40.07 1020.19 65.24 494.39
22.35 54.42 1012.46 75.01 454.72
17.98 56.85 1012.28 84.52 448.71
21.19 42.48 1013.43 80.52 469.76
20.94 44.89 1009.64 75.14 450.71
24.23 58.79 1009.8 75.75 444.01
19.18 58.2 1017.46 76.72 453.2
20.88 57.85 1012.39 85.47 450.87
23.67 63.86 1019.67 57.95 441.73
14.12 39.52 1018.41 78.32 465.09
25.23 64.63 1020.59 52.2 447.28
6.54 39.33 1011.54 93.69 491.16
20.08 62.52 1017.99 75.74 450.98
24.67 63.56 1013.75 67.56 446.3
27.82 79.74 1008.37 69.46 436.48
15.55 42.03 1017.41 74.58 460.84
24.26 69.51 1013.43 53.23 442.56
13.45 41.49 1020.19 88.72 467.3
11.06 40.64 1021.47 96.16 479.13
24.91 52.3 1008.72 68.26 441.15
22.39 59.04 1011.78 86.39 445.52
11.95 40.69 1015.62 85.34 475.4
14.85 40.69 1014.91 72.64 469.3
10.11 41.62 1017.17 97.82 463.57
23.67 68.67 1006.71 77.22 445.32
16.14 44.21 1020.36 80.59 461.03
15.11 43.13 1014.99 46.91 466.74
24.14 59.87 1018.47 57.76 444.04
30.08 67.25 1017.6 53.09 434.01
14.77 44.9 1020.5 84.31 465.23
27.6 69.34 1009.63 71.58 440.6
13.89 44.84 1023.66 92.97 466.74
26.85 75.6 1017.43 74.55 433.48
12.41 40.96 1023.36 78.96 473.59
13.08 41.74 1020.75 64.44 474.81
18.93 44.06 1017.58 68.23 454.75
20.5 49.69 1009.6 70.81 452.94
30.72 69.13 1009.94 61.66 435.83
7.55 39.22 1014.53 77.76 482.19
13.49 44.47 1030.46 69.49 466.66
15.62 40.12 1013.03 96.26 462.59
24.8 64.63 1020.69 55.74 447.82
10.03 41.62 1014.55 95.61 462.73
22.43 63.21 1012.06 84.75 447.98
14.95 39.31 1009.15 75.3 462.72
24.78 58.46 1016.82 67.5 442.42
23.2 48.41 1008.64 80.92 444.69
14.01 39.0 1016.73 79.23 466.7
19.4 64.63 1020.38 81.1 453.84
30.15 67.32 1013.83 32.8 436.92
6.91 36.08 1021.82 84.31 486.37
29.04 60.07 1015.42 46.15 440.43
26.02 63.07 1010.94 53.96 446.82
5.89 39.48 1005.11 59.83 484.91
26.52 71.64 1008.27 75.3 437.76
28.53 68.08 1013.27 42.53 438.91
16.59 39.54 1007.97 70.58 464.19
22.95 67.79 1009.89 91.69 442.19
23.96 47.43 1008.38 63.55 446.86
17.48 44.2 1018.89 61.51 457.15
6.69 43.65 1020.14 69.55 482.57
10.25 41.26 1007.44 98.08 476.03
28.87 72.58 1008.69 79.34 428.89
12.04 40.23 1018.07 81.28 472.7
22.58 52.3 1009.04 78.99 445.6
15.12 52.05 1014.63 80.38 464.78
25.48 58.95 1017.02 51.16 440.42
27.87 70.79 1003.96 72.17 428.41
23.72 70.47 1010.65 75.39 438.5
25.0 59.43 1007.84 68.91 438.28
8.42 40.64 1022.35 96.38 476.29
22.46 58.49 1011.5 70.54 448.46
29.92 57.19 1008.62 45.8 438.99
11.68 39.22 1017.9 57.95 471.8
14.04 42.44 1012.74 81.89 471.81
19.86 59.14 1016.12 69.32 449.82
25.99 68.08 1013.13 59.14 442.14
23.42 58.79 1009.74 81.54 441.46
10.6 40.22 1011.37 85.81 477.62
20.97 61.87 1011.45 65.41 446.76
14.14 39.82 1012.46 81.15 472.52
8.56 40.71 1021.27 95.87 471.58
24.86 72.39 1001.15 90.24 440.85
29.0 77.54 1011.33 75.13 431.37
27.59 71.97 1008.64 88.22 437.33
10.45 40.71 1015.68 81.48 469.22
8.51 40.78 1023.51 89.84 471.11
29.82 66.51 1010.98 43.57 439.17
22.56 62.26 1012.11 63.16 445.33
11.38 39.22 1018.62 57.14 473.71
20.25 57.76 1016.28 77.76 452.66
22.42 59.43 1007.12 90.56 440.99
14.85 38.91 1014.48 60.98 467.42
25.62 58.82 1010.02 70.31 444.14
19.85 56.53 1020.57 74.05 457.17
13.67 54.3 1015.92 75.42 467.87
24.39 70.72 1009.78 82.25 442.04
16.07 44.58 1019.52 67.95 471.36
11.6 39.1 1009.81 100.09 460.7
31.38 70.83 1010.35 47.28 431.33
29.91 76.86 998.59 72.41 432.6
19.67 59.39 1014.07 77.67 447.61
27.18 64.79 1016.27 63.7 443.87
21.39 52.3 1009.2 79.77 446.87
10.45 41.01 1020.57 93.84 465.74
19.46 56.89 1014.02 84.95 447.86
23.55 62.96 1020.16 70.16 447.65
23.35 63.47 1011.78 84.24 437.87
9.26 41.66 1016.87 73.32 483.51
10.3 41.46 1018.21 86.17 479.65
20.94 58.16 1016.88 65.43 455.16
23.13 71.25 1002.49 94.59 431.91
12.77 41.5 1014.13 86.8 470.68
28.29 69.13 1009.29 58.18 429.28
19.13 59.21 1018.32 89.66 450.81
24.44 73.5 1011.49 87.39 437.73
20.32 44.6 1015.16 36.35 460.21
20.54 69.05 1001.6 79.62 442.86
12.16 45.0 1021.51 50.52 482.99
28.09 65.27 1013.27 51.96 440.0
9.25 41.82 1033.25 74.73 478.48
21.75 49.82 1015.01 78.33 455.28
23.7 66.56 1002.07 85.19 436.94
16.22 37.87 1022.36 83.13 461.06
24.75 69.45 1013.97 53.49 438.28
10.48 39.58 1011.81 88.86 472.61
29.53 70.79 1003.7 60.89 426.85
12.59 39.72 1017.76 61.14 470.18
23.5 54.42 1012.31 68.29 455.38
29.01 66.56 1006.44 57.62 428.32
9.75 42.49 1010.57 83.63 480.35
19.55 56.53 1020.2 78.1 455.56
21.05 58.33 1013.14 66.34 447.66
24.72 68.67 1006.74 79.02 443.06
21.19 58.86 1014.19 68.96 452.43
10.77 41.54 1019.94 71.13 477.81
28.68 73.77 1004.72 87.01 431.66
29.87 73.91 1004.53 74.3 431.8
22.99 68.67 1006.65 77.62 446.67
24.66 60.29 1018.0 59.56 445.26
32.63 69.89 1013.85 41.66 425.72
31.38 72.29 1008.73 73.27 430.58
23.87 60.27 1018.94 77.16 439.86
25.6 59.15 1013.31 67.02 441.11
27.62 71.14 1011.6 52.8 434.72
30.1 67.45 1014.23 39.04 434.01
12.19 41.17 1019.43 65.47 475.64
13.11 41.58 1020.43 74.32 460.44
28.29 68.67 1005.46 69.22 436.4
13.45 40.73 1018.7 93.88 461.03
10.98 41.54 1019.94 69.83 479.08
26.48 69.14 1009.31 84.11 435.76
13.07 45.51 1015.22 78.65 460.14
25.56 75.6 1017.37 69.31 442.2
22.68 50.78 1008.83 70.3 447.69
28.86 73.67 1006.65 68.23 431.15
22.7 63.56 1014.32 71.76 445.0
27.89 73.21 1001.32 85.88 431.59
13.78 44.47 1027.94 71.09 467.22
28.14 51.43 1012.16 52.67 445.33
11.8 45.09 1013.21 89.68 470.57
10.71 39.61 1018.72 73.66 473.77
24.54 60.29 1017.42 58.94 447.67
11.54 40.05 1014.78 87.05 474.29
29.47 71.32 1008.07 67.0 437.14
29.24 69.05 1003.12 43.18 432.56
14.51 41.79 1009.72 80.62 459.14
22.91 60.07 1016.03 59.72 446.19
27.02 71.77 1006.38 72.1 428.1
13.49 44.47 1030.18 69.15 468.46
30.24 66.75 1017.95 55.66 435.02
23.19 48.6 1002.38 61.19 445.52
17.73 40.55 1003.36 74.62 462.69
18.62 61.27 1019.26 73.35 455.75
12.85 40.0 1015.89 68.85 463.74
32.33 69.68 1011.95 39.89 439.79
25.09 58.95 1016.99 53.16 443.26
29.45 69.13 1009.3 52.97 432.04
16.91 43.96 1013.32 79.87 465.86
14.09 45.87 1009.05 84.09 465.6
10.73 25.36 1009.35 100.15 469.43
23.2 49.3 1003.4 79.77 440.75
8.21 38.91 1015.82 88.99 481.32
9.3 40.56 1022.64 76.14 479.87
16.97 39.16 1005.7 69.13 458.59
23.69 71.97 1009.62 93.03 438.62
25.13 59.44 1012.38 77.92 445.59
9.86 43.56 1015.13 74.89 481.87
11.33 41.5 1013.58 88.7 475.01
26.95 48.41 1008.53 62.94 436.54
15.0 40.66 1016.28 89.62 456.63
20.76 62.52 1015.63 81.04 451.69
14.29 39.59 1010.93 94.53 463.04
19.74 67.71 1007.68 64.02 446.1
26.68 59.92 1009.94 70.57 438.67
14.24 41.4 1019.7 70.32 466.88
21.98 48.41 1008.42 84.86 444.6
22.75 59.39 1015.4 81.41 440.26
8.34 40.96 1023.28 89.45 483.92
11.8 41.2 1017.18 82.71 475.19
8.81 44.68 1023.06 93.93 479.24
30.05 73.68 1014.95 70.6 434.92
16.01 65.46 1014.0 87.68 454.16
21.75 58.79 1012.42 87.58 447.58
13.94 41.26 1021.67 74.4 467.9
29.25 69.13 1010.27 67.35 426.29
22.33 45.87 1007.8 63.61 447.02
16.43 41.79 1005.47 76.89 455.85
11.5 40.22 1010.31 78.08 476.46
23.53 68.94 1007.53 69.17 437.48
21.86 49.21 1014.61 53.31 452.77
6.17 39.33 1012.57 93.32 491.54
30.19 64.79 1017.22 42.47 438.41
11.67 41.93 1019.81 82.58 476.1
15.34 36.99 1007.87 94.59 464.58
11.5 40.78 1023.91 86.31 467.74
25.53 57.17 1010.0 72.57 442.12
21.27 57.5 1014.53 80.76 453.34
28.37 69.13 1010.44 71.93 425.29
28.39 51.43 1011.74 47.54 449.63
13.78 45.78 1025.27 95.72 462.88
14.6 42.32 1015.71 77.03 464.67
5.1 35.57 1027.17 80.49 489.96
7.0 38.08 1020.27 77.67 482.38
26.3 77.95 1009.45 78.72 437.95
30.56 71.98 1004.74 58.77 429.2
21.09 46.63 1013.03 74.8 453.34
28.21 70.02 1010.58 51.34 442.47
15.84 49.69 1015.14 90.41 462.6
10.03 40.96 1024.57 91.1 478.79
20.37 52.05 1012.34 62.57 456.11
21.19 50.16 1005.81 84.27 450.33
33.73 69.88 1007.21 42.93 434.83
29.87 73.68 1015.1 40.96 433.43
19.62 62.96 1020.76 76.53 456.02
9.93 40.67 1018.08 69.74 485.23
9.43 37.14 1013.03 74.99 473.57
14.24 39.58 1011.17 70.45 469.94
12.97 49.83 1008.69 91.49 452.07
7.6 41.04 1021.82 88.97 475.32
8.39 36.24 1013.39 89.13 480.69
25.41 48.06 1013.12 46.52 444.01
18.43 56.03 1020.41 60.55 465.17
10.31 39.82 1012.87 88.71 480.61
11.29 41.5 1013.39 89.15 476.04
22.61 49.3 1003.51 83.02 441.76
29.34 71.98 1005.19 75.19 428.24
18.87 67.71 1004.0 87.35 444.77
13.21 45.87 1008.58 85.66 463.1
11.3 44.6 1018.19 91.66 470.5
29.23 72.99 1007.04 63.47 431.0
27.76 69.4 1004.27 72.25 430.68
29.26 67.17 1006.6 70.58 436.42
25.72 49.82 1016.19 60.1 452.33
23.43 63.94 1010.64 89.29 440.16
25.6 63.76 1010.18 67.43 435.75
22.3 44.57 1008.48 67.58 449.74
27.91 72.24 1010.74 70.8 430.73
30.35 77.17 1009.55 63.62 432.75
21.78 47.43 1007.88 66.68 446.79
7.19 41.39 1018.12 90.76 486.35
20.88 59.8 1015.66 75.34 453.18
24.19 50.23 1015.73 59.77 458.31
9.98 41.54 1019.7 80.79 480.26
23.47 51.3 1011.89 74.1 448.65
26.35 49.5 1012.67 41.34 458.41
29.89 64.69 1006.37 58.78 435.39
19.29 50.16 1010.49 97.78 450.21
17.48 43.14 1018.68 74.85 459.59
25.21 75.6 1017.19 69.84 445.84
23.3 48.78 1018.17 75.36 441.08
15.42 37.85 1009.89 85.8 467.33
21.44 63.09 1016.56 90.11 444.19
29.45 68.27 1007.96 61.63 432.96
29.69 47.93 1002.85 44.76 438.09
15.52 36.99 1006.86 89.7 467.9
11.47 43.67 1012.68 72.51 475.72
9.77 34.69 1027.72 74.98 477.51
22.6 69.84 1006.37 79.59 435.13
8.24 39.61 1017.99 78.42 477.9
17.01 44.2 1019.18 61.23 457.26
19.64 44.6 1015.88 47.56 467.53
10.61 41.58 1021.08 93.06 465.15
12.04 40.1 1014.42 89.65 474.28
29.19 65.71 1013.85 50.5 444.49
21.75 45.09 1014.15 44.84 452.84
23.66 77.54 1008.5 85.32 435.38
27.05 75.33 1003.88 82.94 433.57
29.63 69.71 1009.04 67.26 435.27
18.2 39.63 1005.35 79.05 468.49
32.22 70.8 1009.9 62.03 433.07
26.88 73.56 1004.85 94.36 430.63
29.05 65.74 1013.29 60.02 440.74
8.9 39.96 1026.31 95.46 474.49
18.93 48.6 1005.72 84.92 449.74
27.49 63.76 1010.09 62.8 436.73
23.1 70.79 1006.53 90.81 434.58
11.22 43.13 1017.24 80.9 473.93
31.97 79.74 1007.03 55.84 435.99
13.32 43.22 1009.45 75.3 466.83
31.68 68.24 1005.29 37.34 427.22
23.69 63.77 1013.39 79.5 444.07
13.83 41.49 1020.11 87.29 469.57
18.32 66.51 1015.18 81.5 459.89
11.05 40.71 1024.91 76.42 479.59
22.03 64.69 1007.21 75.75 440.92
10.23 41.46 1020.45 84.95 480.87
23.92 66.54 1009.93 62.37 441.9
29.38 69.68 1011.35 49.25 430.2
17.35 42.86 1014.62 74.16 465.16
9.81 44.45 1021.19 90.55 471.32
4.97 40.64 1020.91 94.28 485.43
5.15 40.07 1012.27 63.31 495.35
21.54 58.49 1010.85 78.9 449.12
7.94 42.02 1006.22 90.97 480.53
18.77 50.66 1014.89 87.34 457.07
21.69 69.94 1010.7 80.8 443.67
10.07 44.68 1023.44 90.95 477.52
13.83 39.64 1012.52 69.97 472.95
10.45 39.69 1003.92 89.45 472.54
11.56 40.71 1015.85 76.08 469.17
23.64 70.04 1011.09 83.35 435.21
10.48 40.22 1004.81 92.16 477.78
13.09 39.85 1012.86 58.42 475.89
10.67 40.23 1017.75 85.06 483.9
12.57 39.16 1016.53 88.91 476.2
14.45 43.34 1015.47 83.33 462.16
14.22 37.85 1011.24 88.49 471.05
6.97 41.26 1010.6 96.88 484.71
20.61 63.86 1015.43 73.86 446.34
14.67 42.28 1007.21 65.17 469.02
29.06 72.86 1004.23 69.41 432.12
14.38 40.1 1015.51 81.23 467.28
32.51 69.98 1013.29 54.07 429.66
11.79 45.09 1013.16 89.17 469.49
8.65 40.56 1023.23 78.85 485.87
9.75 40.81 1026.0 84.44 481.95
9.11 40.02 1031.1 83.02 479.03
23.39 69.13 1010.99 90.66 434.5
14.3 54.3 1015.16 75.29 464.9
17.49 63.94 1020.02 82.6 452.71
31.1 69.51 1010.84 45.4 429.74
19.77 56.65 1020.67 66.33 457.09
28.61 72.29 1011.61 45.33 446.77
13.52 41.48 1014.46 67.12 460.76
13.52 40.83 1008.31 84.14 471.95
17.57 46.21 1014.09 80.81 453.29
28.18 60.07 1016.34 49.13 441.61
14.29 46.18 1017.01 87.29 464.73
18.12 43.69 1016.91 52.95 464.68
31.27 73.91 1003.72 68.92 430.59
26.24 77.95 1014.19 85.21 438.01
7.44 41.04 1021.84 88.56 479.08
29.78 74.78 1009.28 55.09 436.39
23.37 65.46 1016.25 48.64 447.07
10.62 39.58 1011.9 87.85 479.91
5.84 43.02 1013.88 87.42 489.05
14.51 53.82 1016.46 62.75 463.17
11.31 42.02 1001.18 94.86 471.26
11.25 40.67 1011.64 63.54 480.49
9.18 39.42 1025.41 69.46 473.78
19.82 58.16 1016.76 74.66 455.5
24.77 58.41 1013.78 80.57 446.27
9.66 41.06 1021.21 84.7 482.2
21.96 59.8 1016.72 72.6 452.48
18.59 43.14 1011.92 52.63 464.48
24.75 69.89 1015.29 82.01 438.1
24.37 63.47 1012.77 75.22 445.6
29.6 67.79 1010.37 51.05 442.43
25.32 61.25 1011.56 80.1 436.67
16.15 41.85 1016.54 81.58 466.56
15.74 71.14 1019.65 65.94 457.29
5.97 36.25 1029.65 86.74 487.03
15.84 52.72 1026.45 62.57 464.93
14.84 44.63 1019.28 57.37 466.0
12.25 48.79 1017.44 88.91 469.52
27.38 70.04 1011.18 72.26 428.88
8.76 41.48 1018.49 74.98 474.3
15.54 39.31 1009.69 71.19 461.06
18.71 39.39 1014.09 62.82 465.57
13.06 41.78 1012.3 55.31 467.67
12.72 40.71 1016.02 71.57 466.99
19.83 39.39 1013.73 59.16 463.72
27.23 49.16 1004.03 40.8 443.78
24.27 68.28 1005.43 67.63 445.23
11.8 40.66 1017.13 97.2 464.43
6.76 36.25 1028.31 91.16 484.36
25.99 63.07 1012.5 64.81 442.16
16.3 39.63 1004.64 85.61 464.11
16.5 49.39 1018.35 93.42 462.48
10.59 42.49 1009.59 77.36 477.49
26.05 65.59 1012.78 67.03 437.04
19.5 40.79 1003.8 89.45 457.09
22.21 45.01 1012.22 54.84 450.6
17.86 45.0 1023.25 53.48 465.78
29.96 70.04 1010.15 54.47 427.1
19.08 44.63 1020.14 43.36 459.81
23.59 47.43 1006.64 48.92 447.36
3.38 39.64 1011.0 81.22 488.92
26.39 66.49 1012.96 60.35 433.36
8.99 39.04 1021.99 75.98 483.35
10.91 41.04 1026.57 74.24 469.53
13.08 39.82 1012.27 85.21 476.96
23.95 58.46 1017.5 68.46 440.75
15.64 43.71 1024.51 78.31 462.55
18.78 54.2 1012.05 89.25 448.04
20.65 50.59 1016.22 68.57 455.24
4.96 40.07 1011.8 67.38 494.75
23.51 57.32 1012.55 53.6 444.58
5.99 35.79 1011.56 91.69 484.82
23.65 66.05 1019.6 78.21 442.9
5.17 39.33 1009.68 94.19 485.46
26.38 49.5 1012.82 37.19 457.81
6.02 43.65 1013.85 83.53 481.92
23.2 61.02 1009.63 79.45 443.23
8.57 39.69 1000.91 99.9 474.29
30.72 71.58 1009.98 50.39 430.46
21.52 50.66 1013.56 74.33 455.71
22.93 62.26 1011.25 83.66 438.34
5.71 41.31 1003.24 89.48 485.83
18.62 44.06 1017.76 64.59 452.82
27.88 68.94 1007.68 75.68 435.04
22.32 59.8 1016.82 64.18 451.21
14.55 42.74 1028.41 70.09 465.81
17.83 44.92 1025.04 70.58 458.42
9.68 39.96 1026.09 99.28 470.22
19.41 49.39 1020.84 81.89 449.24
13.22 44.92 1023.84 87.99 471.43
12.24 44.92 1023.74 88.21 473.26
19.21 58.49 1011.7 91.29 452.82
29.74 70.32 1008.1 52.72 432.69
23.28 60.84 1017.91 67.5 444.13
8.02 41.92 1029.8 92.05 467.21
22.47 48.6 1002.33 63.23 445.98
27.51 73.77 1002.42 90.88 436.91
17.51 44.9 1009.05 74.91 455.01
23.22 66.56 1002.47 85.39 437.11
11.73 40.64 1020.68 96.98 477.06
21.19 67.71 1006.65 56.28 441.71
5.48 40.07 1019.63 65.62 495.76
24.26 66.44 1011.33 55.32 445.63
12.32 41.62 1012.88 88.88 464.72
31.26 68.94 1005.94 39.49 438.03
32.09 72.86 1003.47 54.59 434.78
24.98 60.32 1015.63 57.19 444.67
27.48 61.41 1012.2 45.06 452.24
21.04 45.09 1014.19 40.62 450.92
27.75 70.4 1006.65 90.21 436.53
22.79 71.77 1005.75 90.91 435.53
24.22 68.51 1013.23 74.96 440.01
27.06 64.45 1008.72 54.21 443.1
29.25 71.94 1007.18 63.62 427.49
26.86 68.08 1012.99 50.04 436.25
29.64 67.79 1009.99 51.23 440.74
19.92 63.31 1015.02 82.71 443.54
18.5 51.43 1010.82 92.04 459.42
23.71 60.23 1009.76 90.67 439.66
14.39 44.84 1023.55 91.14 464.15
19.3 56.65 1020.55 70.43 459.1
24.65 52.36 1014.76 66.63 455.68
13.5 45.51 1015.33 86.95 469.08
9.82 41.26 1007.71 96.69 478.02
18.4 44.06 1017.36 70.88 456.8
28.12 44.89 1009.18 47.14 441.13
17.15 43.69 1017.05 63.36 463.88
30.69 73.67 1006.14 60.58 430.45
28.82 65.71 1014.24 54.3 449.18
21.3 48.92 1010.92 65.09 447.89
30.58 70.04 1010.4 48.16 431.59
21.17 52.3 1009.36 81.51 447.5
9.87 41.82 1033.04 68.57 475.58
22.18 59.8 1016.77 73.16 453.24
24.39 63.21 1012.59 80.88 446.4
10.73 44.92 1025.1 85.4 476.81
9.38 40.46 1019.29 75.77 474.1
20.27 57.76 1016.66 75.76 450.71
24.82 66.48 1006.4 70.21 433.62
16.55 41.66 1011.45 55.53 465.14
20.73 59.87 1019.08 80.48 445.18
9.51 39.22 1015.3 72.41 474.12
8.63 43.79 1016.08 83.25 483.91
6.48 40.27 1010.55 82.12 486.68
14.95 43.52 1022.43 94.75 464.98
5.76 45.87 1010.83 95.79 481.4
10.94 39.04 1021.81 86.02 479.2
15.87 41.16 1005.85 78.29 463.86
12.42 38.25 1012.76 82.23 472.3
29.12 58.84 1001.31 52.86 446.51
29.12 51.43 1005.93 60.66 437.71
19.08 41.1 1001.96 62.77 458.94
31.06 67.17 1007.62 65.54 437.91
5.72 39.33 1009.96 95.4 490.76
26.52 65.06 1013.4 51.78 439.66
13.84 44.9 1007.58 63.62 463.27
13.03 39.52 1016.68 83.09 473.99
25.94 66.49 1012.83 61.81 433.38
16.64 53.82 1015.13 68.24 459.01
14.13 40.75 1016.05 72.41 471.44
13.65 39.28 1012.97 79.64 471.91
14.5 44.47 1028.2 66.95 465.15
19.8 51.19 1008.25 91.98 446.66
25.2 63.76 1009.78 64.96 438.15
20.66 51.19 1008.81 88.93 447.14
12.07 43.71 1025.53 85.62 472.32
25.64 70.72 1010.16 84.0 441.68
23.33 72.99 1009.33 89.41 440.04
29.41 64.05 1009.82 67.4 444.82
16.6 53.16 1014.5 76.75 457.26
27.53 72.58 1009.13 89.06 428.83
20.62 43.43 1009.93 64.02 449.07
26.02 71.94 1009.38 64.12 435.21
12.75 44.2 1017.59 81.22 471.03
12.87 48.04 1012.47 100.13 465.56
25.77 62.96 1019.86 58.07 442.83
14.84 41.48 1017.26 63.42 460.3
7.41 40.71 1023.07 83.32 474.25
8.87 41.82 1033.3 74.28 477.97
9.69 40.46 1019.1 71.91 472.16
16.17 46.97 1014.22 85.8 456.08
26.24 49.82 1014.9 55.58 452.41
13.78 43.22 1011.31 69.7 463.71
26.3 67.07 1006.26 63.79 433.72
17.37 57.76 1016.0 86.59 456.4
23.6 48.98 1015.41 48.28 448.43
8.3 36.08 1020.63 80.42 481.6
18.86 42.18 1001.16 98.58 457.07
22.12 49.39 1019.8 72.83 451.0
28.41 75.6 1018.48 56.07 440.28
29.42 71.32 1002.26 67.13 437.47
18.61 67.71 1004.07 84.49 443.57
27.57 69.84 1004.91 68.37 426.6
12.83 41.5 1013.12 86.07 470.87
9.64 39.85 1012.9 83.82 478.37
19.13 58.66 1013.32 74.86 453.92
15.92 40.56 1020.79 53.52 470.22
24.64 72.24 1011.37 80.61 434.54
27.62 63.9 1013.11 43.56 442.89
8.9 36.24 1013.29 89.35 479.03
9.55 43.99 1020.5 97.28 476.06
10.57 36.71 1022.62 80.49 473.88
19.8 57.25 1010.84 88.9 451.75
25.63 56.85 1012.68 49.7 439.2
24.7 58.46 1015.58 68.64 439.7
15.26 46.18 1013.68 98.58 463.6
20.06 52.84 1004.21 82.12 447.47
19.84 56.89 1013.23 78.32 447.92
11.49 44.63 1020.44 86.04 471.08
23.74 72.43 1007.99 91.36 437.55
22.62 51.3 1012.36 81.02 448.27
29.53 72.39 998.47 76.05 431.69
21.32 48.14 1016.57 71.81 449.09
20.3 58.46 1015.93 82.13 448.79
16.97 44.92 1025.21 74.27 460.21
12.07 41.17 1013.54 71.32 479.28
7.46 41.82 1032.67 74.59 483.11
19.2 54.2 1011.46 84.44 450.75
28.64 66.54 1010.43 43.39 437.97
13.56 41.48 1008.53 87.2 459.76
17.4 44.9 1020.5 77.11 457.75
14.08 40.1 1015.48 82.81 469.33
27.11 69.75 1009.74 85.67 433.28
20.92 70.02 1010.23 95.58 444.64
16.18 44.9 1021.3 74.46 463.1
15.57 44.68 1022.01 90.02 460.91
10.37 39.04 1023.95 81.93 479.35
19.6 59.21 1017.65 86.29 449.23
9.22 40.92 1021.83 85.43 474.51
27.76 72.99 1007.81 71.66 435.02
28.68 70.72 1009.43 71.33 435.45
20.95 48.14 1013.3 67.72 452.38
9.06 39.3 1019.73 84.23 480.41
9.21 39.72 1019.54 74.44 478.96
13.65 42.74 1026.58 71.48 468.87
31.79 76.2 1007.89 56.3 434.01
14.32 44.6 1013.85 68.13 466.36
26.28 75.23 1011.44 68.35 435.28
7.69 43.02 1014.51 85.23 486.46
14.44 40.1 1015.51 79.78 468.19
9.19 41.01 1022.14 98.98 468.37
13.35 41.39 1019.17 72.87 474.19
23.04 74.22 1009.52 90.93 440.32
4.83 38.44 1015.35 72.94 485.32
17.29 42.86 1014.38 72.3 464.27
8.73 36.18 1013.66 77.74 479.25
26.21 70.32 1007.0 78.29 430.4
23.72 58.62 1016.65 69.1 447.49
29.27 64.69 1006.85 55.79 438.23
10.4 40.43 1025.46 75.09 492.09
12.19 40.75 1015.13 88.98 475.36
20.4 54.9 1016.68 64.26 452.56
34.3 74.67 1015.98 25.89 427.84
27.56 68.08 1010.8 59.18 433.95
30.9 70.8 1008.48 67.48 435.27
14.85 58.59 1014.04 89.85 454.62
16.42 40.56 1020.36 50.62 472.17
16.45 63.31 1015.96 83.97 452.42
10.14 42.02 1003.19 96.51 472.17
9.53 41.44 1018.01 80.09 481.83
17.01 49.15 1021.83 84.02 458.78
23.94 62.08 1022.47 61.97 447.5
15.95 49.25 1019.04 88.51 463.4
11.15 41.26 1022.67 81.83 473.57
25.56 70.32 1009.07 90.63 433.72
27.16 66.44 1011.2 73.37 431.85
26.71 77.95 1012.13 77.5 433.47
29.56 74.22 1007.45 57.46 432.84
31.19 70.94 1007.29 51.91 436.6
6.86 41.17 1020.12 79.14 490.23
12.36 41.74 1020.58 69.24 477.16
32.82 68.31 1010.44 41.85 441.06
25.3 70.98 1007.22 95.1 440.86
8.71 41.82 1033.08 74.53 477.94
13.34 40.8 1026.56 64.85 474.47
14.2 43.02 1012.18 57.07 470.67
23.74 65.34 1013.7 62.9 447.31
16.9 44.88 1018.14 72.21 466.8
28.54 71.94 1007.4 65.99 430.91
30.15 69.88 1007.2 73.67 434.75
14.33 42.86 1010.82 88.59 469.52
25.57 59.43 1008.88 61.19 438.9
30.55 70.04 1010.51 49.37 429.56
28.04 74.33 1013.53 48.65 432.92
26.39 49.16 1005.68 56.18 442.87
15.3 41.76 1022.57 71.56 466.59
6.03 41.14 1028.04 87.46 479.61
13.49 44.63 1019.12 70.02 471.08
27.67 59.14 1016.51 61.2 433.37
24.19 65.48 1018.8 60.54 443.92
24.44 59.14 1016.74 71.82 443.5
29.86 64.79 1017.37 44.8 439.89
30.2 69.59 1008.9 67.32 434.66
7.99 41.38 1021.95 78.77 487.57
9.93 41.62 1013.76 96.02 464.64
11.03 42.32 1017.26 90.56 470.92
22.34 63.73 1014.37 83.19 444.39
25.33 48.6 1002.54 68.45 442.48
18.87 52.08 1005.25 99.19 449.61
25.97 69.34 1009.43 88.11 435.02
16.58 43.99 1021.81 79.29 458.67
14.35 46.18 1016.63 87.76 461.74
25.06 62.39 1008.09 82.56 438.31
13.85 48.92 1011.68 79.24 462.38
16.09 44.2 1019.39 67.24 460.56
26.34 59.21 1013.37 58.98 439.22
23.01 58.79 1009.71 84.22 444.64
26.39 71.25 999.8 89.12 430.34
31.32 71.29 1008.37 50.07 430.46
16.64 45.87 1009.02 98.86 456.79
13.42 41.23 994.17 95.79 468.82
20.06 44.9 1008.79 70.06 448.51
14.8 44.71 1014.67 41.71 470.77
12.59 41.14 1025.79 86.55 465.74
26.7 66.56 1005.31 71.97 430.21
19.78 50.32 1008.62 96.4 449.23
15.17 49.15 1021.91 91.73 461.89
21.71 61.45 1010.97 91.62 445.72
19.09 39.39 1013.36 59.14 466.13
19.76 51.19 1008.38 92.56 448.71
14.68 41.23 998.43 83.71 469.25
21.3 66.86 1013.04 55.43 450.56
16.73 39.64 1008.94 74.91 464.46
12.26 41.5 1014.87 89.41 471.13
14.77 48.06 1010.92 69.81 461.52
18.26 59.15 1012.04 86.01 451.09
27.1 79.74 1005.43 86.05 431.51
14.72 40.83 1009.65 80.98 469.8
26.3 51.43 1012.05 63.62 442.28
16.48 48.92 1011.84 64.16 458.67
17.99 43.79 1016.13 75.63 462.4
20.34 59.8 1015.18 80.21 453.54
25.53 62.96 1019.81 59.7 444.38
31.59 58.9 1003.39 47.6 440.52
30.8 69.14 1007.68 63.78 433.62
10.75 45.0 1023.68 89.37 481.96
19.3 44.9 1008.89 70.55 452.75
4.71 39.42 1026.4 84.42 481.28
23.1 66.05 1020.28 80.62 439.03
32.63 73.88 1005.64 52.56 435.75
26.63 74.16 1009.72 83.26 436.03
24.35 58.49 1011.03 70.64 445.6
15.11 56.03 1020.27 89.95 462.65
29.1 50.05 1005.87 51.53 438.66
21.24 50.32 1008.54 84.83 447.32
6.16 39.48 1004.85 59.68 484.55
7.36 41.01 1024.9 97.88 476.8
10.44 39.04 1023.99 85.03 480.34
26.76 48.41 1010.53 47.38 440.63
16.79 44.6 1014.27 48.08 459.48
10.76 40.43 1025.98 79.65 490.78
6.07 38.91 1019.25 83.39 483.56
27.33 73.18 1012.26 82.18 429.38
27.15 59.21 1013.49 51.71 440.27
22.35 51.43 1011.34 77.33 445.34
21.82 65.27 1013.86 72.81 447.43
21.11 69.94 1004.37 84.26 439.91
19.95 50.59 1016.11 73.23 459.27
7.45 39.61 1017.88 79.73 478.89
15.36 41.66 1012.41 62.32 466.7
15.65 43.5 1021.39 78.58 463.5
25.31 74.33 1015.04 79.88 436.21
25.88 63.47 1011.95 65.87 443.94
24.6 63.94 1012.87 80.28 439.63
22.58 41.54 1013.21 71.33 460.95
19.69 59.14 1015.99 70.33 448.69
25.85 75.08 1006.24 57.73 444.63
10.06 37.83 1005.49 99.46 473.51
18.59 39.54 1008.56 68.61 462.56
18.27 50.16 1011.07 95.91 451.76
8.85 40.43 1025.68 80.42 491.81
30.04 68.08 1011.04 51.01 429.52
26.06 49.02 1007.59 74.08 437.9
14.8 38.73 1003.18 80.73 467.54
23.93 64.45 1015.35 54.71 449.97
23.72 66.48 1003.61 73.75 436.62
11.44 40.55 1023.37 88.43 477.68
20.28 63.86 1016.04 74.66 447.26
27.9 63.13 1011.8 70.04 439.76
24.74 59.39 1015.23 74.64 437.49
14.8 58.2 1018.29 85.11 455.14
8.22 41.03 1021.76 82.97 485.5
27.56 66.93 1016.81 55.59 444.1
32.07 70.94 1006.91 49.9 432.33
9.53 44.03 1008.87 89.99 471.23
13.61 42.34 1017.93 91.61 463.89
22.2 51.19 1009.2 82.95 445.54
21.36 59.54 1007.99 92.62 446.09
23.25 63.86 1017.82 59.64 445.12
23.5 59.21 1018.29 63.0 443.31
8.46 39.66 1015.14 85.38 484.16
8.19 40.69 1019.86 85.23 477.76
30.67 71.29 1008.36 52.08 430.28
32.48 62.04 1010.39 38.05 446.48
8.99 36.66 1028.11 71.98 481.03
13.77 47.83 1007.41 90.66 466.07
19.05 67.32 1013.2 83.14 447.47
21.19 55.5 1019.83 65.22 455.93
10.12 40.0 1021.15 91.67 479.62
24.93 47.01 1014.28 66.04 455.06
8.47 40.46 1019.87 78.19 475.06
24.52 56.85 1012.59 54.47 438.89
28.55 69.84 1003.38 67.26 432.7
20.58 50.9 1011.89 72.56 452.6
18.31 46.21 1010.46 82.15 451.75
27.18 71.06 1008.16 86.32 430.66
4.43 38.91 1019.04 88.17 491.9
26.02 74.78 1010.04 72.78 439.82
15.75 39.0 1015.91 69.58 460.73
22.99 60.95 1015.14 69.86 449.7
25.52 59.15 1013.88 65.37 439.42
27.04 65.06 1013.33 52.37 439.84
6.42 35.57 1025.58 79.63 485.86
17.04 40.12 1011.81 83.14 458.1
10.79 39.82 1012.89 88.25 479.92
20.41 56.03 1019.94 55.85 458.29
7.36 40.07 1017.29 52.55 489.45
28.08 73.42 1012.17 62.74 434.0
24.74 69.13 1010.69 90.08 431.24
28.32 47.93 1003.26 54.5 439.5
16.71 40.56 1019.48 49.88 467.46
30.7 71.58 1010.0 48.96 429.27
18.42 58.95 1016.95 86.77 452.1
10.62 42.02 999.83 96.66 472.41
22.18 69.05 1002.75 70.84 442.14
22.38 49.3 1003.56 83.83 441.0
13.94 41.58 1020.76 68.22 463.07
21.24 60.84 1017.99 82.22 445.71
6.76 39.81 1017.11 87.9 483.16
26.73 68.84 1010.75 66.83 440.45
7.24 38.06 1020.6 85.36 481.83
10.84 40.62 1015.53 60.9 467.6
19.32 52.84 1004.29 83.51 450.88
29.0 69.13 1001.22 52.96 425.5
23.38 54.42 1013.95 73.02 451.87
31.17 69.51 1010.51 43.11 428.94
26.17 48.6 1002.59 61.41 439.86
30.9 73.42 1011.21 65.32 433.44
24.92 73.68 1015.12 93.68 438.23
32.77 71.32 1007.68 42.39 436.95
14.37 40.56 1021.67 68.18 470.19
8.36 40.22 1011.6 89.18 484.66
31.45 68.27 1007.56 64.79 430.81
31.6 73.17 1010.05 43.48 433.37
17.9 48.98 1014.17 80.4 453.02
20.35 50.9 1012.6 72.43 453.5
16.21 41.23 995.88 80.0 463.09
19.36 44.6 1016.25 45.65 464.56
21.04 65.46 1017.22 63.02 452.12
14.05 40.69 1015.66 74.39 470.9
23.48 64.15 1021.08 57.77 450.89
21.91 63.76 1009.85 76.8 445.04
24.42 63.07 1011.49 67.39 444.72
14.26 40.92 1022.07 73.96 460.38
21.38 58.33 1013.05 72.75 446.8
15.71 44.06 1018.34 71.69 465.05
5.78 40.62 1016.55 84.98 484.13
6.77 39.81 1017.01 87.68 488.27
23.84 49.21 1013.85 50.36 447.09
21.17 58.16 1017.16 68.11 452.02
19.94 58.96 1014.16 66.27 455.55
8.73 41.92 1029.41 89.72 480.99
16.39 41.67 1012.96 61.07 467.68
col_name data_type comment
AT double null
V double null
AP double null
RH double null
PE double null
summary AT V AP RH PE
count 9568 9568 9568 9568 9568
mean 19.65123118729102 54.30580372073601 1013.2590781772603 73.30897784280926 454.3650094063554
stddev 7.4524732296110825 12.707892998326784 5.938783705811581 14.600268756728964 17.066994999803402
min 1.81 25.36 992.89 25.56 420.26
max 37.11 81.56 1033.3 100.16 495.76
Temperature Power
14.96 463.26
25.18 444.37
5.11 488.56
20.86 446.48
10.82 473.9
26.27 443.67
15.89 467.35
9.48 478.42
14.64 475.98
11.74 477.5
17.99 453.02
20.14 453.99
24.34 440.29
25.71 451.28
26.19 433.99
21.42 462.19
18.21 467.54
11.04 477.2
14.45 459.85
13.97 464.3
17.76 468.27
5.41 495.24
7.76 483.8
27.23 443.61
27.36 436.06
27.47 443.25
14.6 464.16
7.91 475.52
5.81 484.41
30.53 437.89
23.87 445.11
26.09 438.86
29.27 440.98
27.38 436.65
24.81 444.26
12.75 465.86
24.66 444.37
16.38 450.69
13.91 469.02
23.18 448.86
22.47 447.14
13.39 469.18
9.28 482.8
11.82 476.7
10.27 474.99
22.92 444.22
16.0 461.33
21.22 448.06
13.46 474.6
9.39 473.05
31.07 432.06
12.82 467.41
32.57 430.12
8.11 473.62
13.92 471.81
23.04 442.99
27.31 442.77
5.91 491.49
25.26 447.46
27.97 446.11
26.08 442.44
29.01 446.22
12.18 471.49
13.76 463.5
25.5 440.01
28.26 441.03
21.39 452.68
7.26 474.91
10.54 478.77
27.71 434.2
23.11 437.91
7.51 477.61
26.46 431.65
29.34 430.57
10.32 481.09
22.74 445.56
13.48 475.74
25.52 435.12
21.58 446.15
27.66 436.64
26.96 436.69
12.29 468.75
15.86 466.6
13.87 465.48
24.09 441.34
20.45 441.83
15.07 464.7
32.72 437.99
18.23 459.12
35.56 429.69
18.36 459.8
26.35 433.63
25.92 442.84
8.01 485.13
19.63 459.12
20.02 445.31
10.08 480.8
27.23 432.55
23.37 443.86
18.74 449.77
14.81 470.71
23.1 452.17
10.72 478.29
29.46 428.54
8.1 478.27
27.29 439.58
17.1 457.32
11.49 475.51
23.69 439.66
13.51 471.99
9.64 479.81
25.65 434.78
21.59 446.58
27.98 437.76
18.8 459.36
18.28 462.28
13.55 464.33
22.99 444.36
23.94 438.64
13.74 470.49
21.3 455.13
27.54 450.22
24.81 440.43
4.97 482.98
15.22 460.44
23.88 444.97
33.01 433.94
25.98 439.73
28.18 434.48
21.67 442.33
17.67 457.67
21.37 454.66
28.69 432.21
16.61 457.66
27.91 435.21
20.97 448.22
10.8 475.51
20.61 446.53
25.45 441.3
30.16 433.54
4.99 472.52
10.51 474.77
33.79 435.1
21.34 450.74
23.4 442.7
32.21 426.56
14.26 463.71
27.71 447.06
21.95 452.27
25.76 445.78
23.68 438.65
8.28 480.15
23.44 447.19
25.32 443.04
3.94 488.81
17.3 455.75
18.2 455.86
21.43 457.68
11.16 479.11
30.38 432.84
23.36 448.37
21.69 447.06
23.62 443.53
21.87 445.21
29.25 441.7
20.03 450.93
18.14 451.44
24.23 441.29
18.11 458.85
6.57 481.46
12.56 467.19
13.4 461.54
27.1 439.08
14.28 467.22
16.29 468.8
31.24 426.93
10.57 474.65
13.8 468.97
25.3 433.97
18.06 450.53
25.42 444.51
15.07 469.03
11.75 466.56
20.23 457.57
27.31 440.13
28.57 433.24
17.9 452.55
23.83 443.29
27.92 431.76
17.34 454.97
17.94 456.7
6.4 486.03
11.78 472.79
20.28 452.03
21.04 443.41
25.11 441.93
30.28 432.64
8.14 480.25
16.86 466.68
6.25 494.39
22.35 454.72
17.98 448.71
21.19 469.76
20.94 450.71
24.23 444.01
19.18 453.2
20.88 450.87
23.67 441.73
14.12 465.09
25.23 447.28
6.54 491.16
20.08 450.98
24.67 446.3
27.82 436.48
15.55 460.84
24.26 442.56
13.45 467.3
11.06 479.13
24.91 441.15
22.39 445.52
11.95 475.4
14.85 469.3
10.11 463.57
23.67 445.32
16.14 461.03
15.11 466.74
24.14 444.04
30.08 434.01
14.77 465.23
27.6 440.6
13.89 466.74
26.85 433.48
12.41 473.59
13.08 474.81
18.93 454.75
20.5 452.94
30.72 435.83
7.55 482.19
13.49 466.66
15.62 462.59
24.8 447.82
10.03 462.73
22.43 447.98
14.95 462.72
24.78 442.42
23.2 444.69
14.01 466.7
19.4 453.84
30.15 436.92
6.91 486.37
29.04 440.43
26.02 446.82
5.89 484.91
26.52 437.76
28.53 438.91
16.59 464.19
22.95 442.19
23.96 446.86
17.48 457.15
6.69 482.57
10.25 476.03
28.87 428.89
12.04 472.7
22.58 445.6
15.12 464.78
25.48 440.42
27.87 428.41
23.72 438.5
25.0 438.28
8.42 476.29
22.46 448.46
29.92 438.99
11.68 471.8
14.04 471.81
19.86 449.82
25.99 442.14
23.42 441.46
10.6 477.62
20.97 446.76
14.14 472.52
8.56 471.58
24.86 440.85
29.0 431.37
27.59 437.33
10.45 469.22
8.51 471.11
29.82 439.17
22.56 445.33
11.38 473.71
20.25 452.66
22.42 440.99
14.85 467.42
25.62 444.14
19.85 457.17
13.67 467.87
24.39 442.04
16.07 471.36
11.6 460.7
31.38 431.33
29.91 432.6
19.67 447.61
27.18 443.87
21.39 446.87
10.45 465.74
19.46 447.86
23.55 447.65
23.35 437.87
9.26 483.51
10.3 479.65
20.94 455.16
23.13 431.91
12.77 470.68
28.29 429.28
19.13 450.81
24.44 437.73
20.32 460.21
20.54 442.86
12.16 482.99
28.09 440.0
9.25 478.48
21.75 455.28
23.7 436.94
16.22 461.06
24.75 438.28
10.48 472.61
29.53 426.85
12.59 470.18
23.5 455.38
29.01 428.32
9.75 480.35
19.55 455.56
21.05 447.66
24.72 443.06
21.19 452.43
10.77 477.81
28.68 431.66
29.87 431.8
22.99 446.67
24.66 445.26
32.63 425.72
31.38 430.58
23.87 439.86
25.6 441.11
27.62 434.72
30.1 434.01
12.19 475.64
13.11 460.44
28.29 436.4
13.45 461.03
10.98 479.08
26.48 435.76
13.07 460.14
25.56 442.2
22.68 447.69
28.86 431.15
22.7 445.0
27.89 431.59
13.78 467.22
28.14 445.33
11.8 470.57
10.71 473.77
24.54 447.67
11.54 474.29
29.47 437.14
29.24 432.56
14.51 459.14
22.91 446.19
27.02 428.1
13.49 468.46
30.24 435.02
23.19 445.52
17.73 462.69
18.62 455.75
12.85 463.74
32.33 439.79
25.09 443.26
29.45 432.04
16.91 465.86
14.09 465.6
10.73 469.43
23.2 440.75
8.21 481.32
9.3 479.87
16.97 458.59
23.69 438.62
25.13 445.59
9.86 481.87
11.33 475.01
26.95 436.54
15.0 456.63
20.76 451.69
14.29 463.04
19.74 446.1
26.68 438.67
14.24 466.88
21.98 444.6
22.75 440.26
8.34 483.92
11.8 475.19
8.81 479.24
30.05 434.92
16.01 454.16
21.75 447.58
13.94 467.9
29.25 426.29
22.33 447.02
16.43 455.85
11.5 476.46
23.53 437.48
21.86 452.77
6.17 491.54
30.19 438.41
11.67 476.1
15.34 464.58
11.5 467.74
25.53 442.12
21.27 453.34
28.37 425.29
28.39 449.63
13.78 462.88
14.6 464.67
5.1 489.96
7.0 482.38
26.3 437.95
30.56 429.2
21.09 453.34
28.21 442.47
15.84 462.6
10.03 478.79
20.37 456.11
21.19 450.33
33.73 434.83
29.87 433.43
19.62 456.02
9.93 485.23
9.43 473.57
14.24 469.94
12.97 452.07
7.6 475.32
8.39 480.69
25.41 444.01
18.43 465.17
10.31 480.61
11.29 476.04
22.61 441.76
29.34 428.24
18.87 444.77
13.21 463.1
11.3 470.5
29.23 431.0
27.76 430.68
29.26 436.42
25.72 452.33
23.43 440.16
25.6 435.75
22.3 449.74
27.91 430.73
30.35 432.75
21.78 446.79
7.19 486.35
20.88 453.18
24.19 458.31
9.98 480.26
23.47 448.65
26.35 458.41
29.89 435.39
19.29 450.21
17.48 459.59
25.21 445.84
23.3 441.08
15.42 467.33
21.44 444.19
29.45 432.96
29.69 438.09
15.52 467.9
11.47 475.72
9.77 477.51
22.6 435.13
8.24 477.9
17.01 457.26
19.64 467.53
10.61 465.15
12.04 474.28
29.19 444.49
21.75 452.84
23.66 435.38
27.05 433.57
29.63 435.27
18.2 468.49
32.22 433.07
26.88 430.63
29.05 440.74
8.9 474.49
18.93 449.74
27.49 436.73
23.1 434.58
11.22 473.93
31.97 435.99
13.32 466.83
31.68 427.22
23.69 444.07
13.83 469.57
18.32 459.89
11.05 479.59
22.03 440.92
10.23 480.87
23.92 441.9
29.38 430.2
17.35 465.16
9.81 471.32
4.97 485.43
5.15 495.35
21.54 449.12
7.94 480.53
18.77 457.07
21.69 443.67
10.07 477.52
13.83 472.95
10.45 472.54
11.56 469.17
23.64 435.21
10.48 477.78
13.09 475.89
10.67 483.9
12.57 476.2
14.45 462.16
14.22 471.05
6.97 484.71
20.61 446.34
14.67 469.02
29.06 432.12
14.38 467.28
32.51 429.66
11.79 469.49
8.65 485.87
9.75 481.95
9.11 479.03
23.39 434.5
14.3 464.9
17.49 452.71
31.1 429.74
19.77 457.09
28.61 446.77
13.52 460.76
13.52 471.95
17.57 453.29
28.18 441.61
14.29 464.73
18.12 464.68
31.27 430.59
26.24 438.01
7.44 479.08
29.78 436.39
23.37 447.07
10.62 479.91
5.84 489.05
14.51 463.17
11.31 471.26
11.25 480.49
9.18 473.78
19.82 455.5
24.77 446.27
9.66 482.2
21.96 452.48
18.59 464.48
24.75 438.1
24.37 445.6
29.6 442.43
25.32 436.67
16.15 466.56
15.74 457.29
5.97 487.03
15.84 464.93
14.84 466.0
12.25 469.52
27.38 428.88
8.76 474.3
15.54 461.06
18.71 465.57
13.06 467.67
12.72 466.99
19.83 463.72
27.23 443.78
24.27 445.23
11.8 464.43
6.76 484.36
25.99 442.16
16.3 464.11
16.5 462.48
10.59 477.49
26.05 437.04
19.5 457.09
22.21 450.6
17.86 465.78
29.96 427.1
19.08 459.81
23.59 447.36
3.38 488.92
26.39 433.36
8.99 483.35
10.91 469.53
13.08 476.96
23.95 440.75
15.64 462.55
18.78 448.04
20.65 455.24
4.96 494.75
23.51 444.58
5.99 484.82
23.65 442.9
5.17 485.46
26.38 457.81
6.02 481.92
23.2 443.23
8.57 474.29
30.72 430.46
21.52 455.71
22.93 438.34
5.71 485.83
18.62 452.82
27.88 435.04
22.32 451.21
14.55 465.81
17.83 458.42
9.68 470.22
19.41 449.24
13.22 471.43
12.24 473.26
19.21 452.82
29.74 432.69
23.28 444.13
8.02 467.21
22.47 445.98
27.51 436.91
17.51 455.01
23.22 437.11
11.73 477.06
21.19 441.71
5.48 495.76
24.26 445.63
12.32 464.72
31.26 438.03
32.09 434.78
24.98 444.67
27.48 452.24
21.04 450.92
27.75 436.53
22.79 435.53
24.22 440.01
27.06 443.1
29.25 427.49
26.86 436.25
29.64 440.74
19.92 443.54
18.5 459.42
23.71 439.66
14.39 464.15
19.3 459.1
24.65 455.68
13.5 469.08
9.82 478.02
18.4 456.8
28.12 441.13
17.15 463.88
30.69 430.45
28.82 449.18
21.3 447.89
30.58 431.59
21.17 447.5
9.87 475.58
22.18 453.24
24.39 446.4
10.73 476.81
9.38 474.1
20.27 450.71
24.82 433.62
16.55 465.14
20.73 445.18
9.51 474.12
8.63 483.91
6.48 486.68
14.95 464.98
5.76 481.4
10.94 479.2
15.87 463.86
12.42 472.3
29.12 446.51
29.12 437.71
19.08 458.94
31.06 437.91
5.72 490.76
26.52 439.66
13.84 463.27
13.03 473.99
25.94 433.38
16.64 459.01
14.13 471.44
13.65 471.91
14.5 465.15
19.8 446.66
25.2 438.15
20.66 447.14
12.07 472.32
25.64 441.68
23.33 440.04
29.41 444.82
16.6 457.26
27.53 428.83
20.62 449.07
26.02 435.21
12.75 471.03
12.87 465.56
25.77 442.83
14.84 460.3
7.41 474.25
8.87 477.97
9.69 472.16
16.17 456.08
26.24 452.41
13.78 463.71
26.3 433.72
17.37 456.4
23.6 448.43
8.3 481.6
18.86 457.07
22.12 451.0
28.41 440.28
29.42 437.47
18.61 443.57
27.57 426.6
12.83 470.87
9.64 478.37
19.13 453.92
15.92 470.22
24.64 434.54
27.62 442.89
8.9 479.03
9.55 476.06
10.57 473.88
19.8 451.75
25.63 439.2
24.7 439.7
15.26 463.6
20.06 447.47
19.84 447.92
11.49 471.08
23.74 437.55
22.62 448.27
29.53 431.69
21.32 449.09
20.3 448.79
16.97 460.21
12.07 479.28
7.46 483.11
19.2 450.75
28.64 437.97
13.56 459.76
17.4 457.75
14.08 469.33
27.11 433.28
20.92 444.64
16.18 463.1
15.57 460.91
10.37 479.35
19.6 449.23
9.22 474.51
27.76 435.02
28.68 435.45
20.95 452.38
9.06 480.41
9.21 478.96
13.65 468.87
31.79 434.01
14.32 466.36
26.28 435.28
7.69 486.46
14.44 468.19
9.19 468.37
13.35 474.19
23.04 440.32
4.83 485.32
17.29 464.27
8.73 479.25
26.21 430.4
23.72 447.49
29.27 438.23
10.4 492.09
12.19 475.36
20.4 452.56
34.3 427.84
27.56 433.95
30.9 435.27
14.85 454.62
16.42 472.17
16.45 452.42
10.14 472.17
9.53 481.83
17.01 458.78
23.94 447.5
15.95 463.4
11.15 473.57
25.56 433.72
27.16 431.85
26.71 433.47
29.56 432.84
31.19 436.6
6.86 490.23
12.36 477.16
32.82 441.06
25.3 440.86
8.71 477.94
13.34 474.47
14.2 470.67
23.74 447.31
16.9 466.8
28.54 430.91
30.15 434.75
14.33 469.52
25.57 438.9
30.55 429.56
28.04 432.92
26.39 442.87
15.3 466.59
6.03 479.61
13.49 471.08
27.67 433.37
24.19 443.92
24.44 443.5
29.86 439.89
30.2 434.66
7.99 487.57
9.93 464.64
11.03 470.92
22.34 444.39
25.33 442.48
18.87 449.61
25.97 435.02
16.58 458.67
14.35 461.74
25.06 438.31
13.85 462.38
16.09 460.56
26.34 439.22
23.01 444.64
26.39 430.34
31.32 430.46
16.64 456.79
13.42 468.82
20.06 448.51
14.8 470.77
12.59 465.74
26.7 430.21
19.78 449.23
15.17 461.89
21.71 445.72
19.09 466.13
19.76 448.71
14.68 469.25
21.3 450.56
16.73 464.46
12.26 471.13
14.77 461.52
18.26 451.09
27.1 431.51
14.72 469.8
26.3 442.28
16.48 458.67
17.99 462.4
20.34 453.54
25.53 444.38
31.59 440.52
30.8 433.62
10.75 481.96
19.3 452.75
4.71 481.28
23.1 439.03
32.63 435.75
26.63 436.03
24.35 445.6
15.11 462.65
29.1 438.66
21.24 447.32
6.16 484.55
7.36 476.8
10.44 480.34
26.76 440.63
16.79 459.48
10.76 490.78
6.07 483.56
27.33 429.38
27.15 440.27
22.35 445.34
21.82 447.43
21.11 439.91
19.95 459.27
7.45 478.89
15.36 466.7
15.65 463.5
25.31 436.21
25.88 443.94
24.6 439.63
22.58 460.95
19.69 448.69
25.85 444.63
10.06 473.51
18.59 462.56
18.27 451.76
8.85 491.81
30.04 429.52
26.06 437.9
14.8 467.54
23.93 449.97
23.72 436.62
11.44 477.68
20.28 447.26
27.9 439.76
24.74 437.49
14.8 455.14
8.22 485.5
27.56 444.1
32.07 432.33
9.53 471.23
13.61 463.89
22.2 445.54
21.36 446.09
23.25 445.12
23.5 443.31
8.46 484.16
8.19 477.76
30.67 430.28
32.48 446.48
8.99 481.03
13.77 466.07
19.05 447.47
21.19 455.93
10.12 479.62
24.93 455.06
8.47 475.06
24.52 438.89
28.55 432.7
20.58 452.6
18.31 451.75
27.18 430.66
4.43 491.9
26.02 439.82
15.75 460.73
22.99 449.7
25.52 439.42
27.04 439.84
6.42 485.86
17.04 458.1
10.79 479.92
20.41 458.29
7.36 489.45
28.08 434.0
24.74 431.24
28.32 439.5
16.71 467.46
30.7 429.27
18.42 452.1
10.62 472.41
22.18 442.14
22.38 441.0
13.94 463.07
21.24 445.71
6.76 483.16
26.73 440.45
7.24 481.83
10.84 467.6
19.32 450.88
29.0 425.5
23.38 451.87
31.17 428.94
26.17 439.86
30.9 433.44
24.92 438.23
32.77 436.95
14.37 470.19
8.36 484.66
31.45 430.81
31.6 433.37
17.9 453.02
20.35 453.5
16.21 463.09
19.36 464.56
21.04 452.12
14.05 470.9
23.48 450.89
21.91 445.04
24.42 444.72
14.26 460.38
21.38 446.8
15.71 465.05
5.78 484.13
6.77 488.27
23.84 447.09
21.17 452.02
19.94 455.55
8.73 480.99
16.39 467.68
ExhaustVaccum Power
41.76 463.26
62.96 444.37
39.4 488.56
57.32 446.48
37.5 473.9
59.44 443.67
43.96 467.35
44.71 478.42
45.0 475.98
43.56 477.5
43.72 453.02
46.93 453.99
73.5 440.29
58.59 451.28
69.34 433.99
43.79 462.19
45.0 467.54
41.74 477.2
52.75 459.85
38.47 464.3
42.42 468.27
40.07 495.24
42.28 483.8
63.9 443.61
48.6 436.06
70.72 443.25
39.31 464.16
39.96 475.52
35.79 484.41
65.18 437.89
63.94 445.11
58.41 438.86
66.85 440.98
74.16 436.65
63.94 444.26
44.03 465.86
63.73 444.37
47.45 450.69
39.35 469.02
51.3 448.86
47.45 447.14
44.85 469.18
41.54 482.8
42.86 476.7
40.64 474.99
63.94 444.22
37.87 461.33
43.43 448.06
44.71 474.6
40.11 473.05
73.5 432.06
38.62 467.41
78.92 430.12
42.18 473.62
39.39 471.81
59.43 442.99
64.44 442.77
39.33 491.49
61.08 447.46
58.84 446.11
52.3 442.44
65.71 446.22
40.1 471.49
45.87 463.5
58.79 440.01
65.34 441.03
62.96 452.68
40.69 474.91
34.03 478.77
74.34 434.2
68.3 437.91
41.01 477.61
74.67 431.65
74.34 430.57
42.28 481.09
61.02 445.56
39.85 475.74
69.75 435.12
67.25 446.15
76.86 436.64
69.45 436.69
42.18 468.75
43.02 466.6
45.08 465.48
73.68 441.34
69.45 441.83
39.3 464.7
69.75 437.99
58.96 459.12
68.94 429.69
51.43 459.8
64.05 433.63
60.95 442.84
41.66 485.13
52.72 459.12
67.32 445.31
40.72 480.8
66.48 432.55
63.77 443.86
59.21 449.77
43.69 470.71
51.3 452.17
41.38 478.29
71.94 428.54
40.64 478.27
62.66 439.58
49.69 457.32
44.2 475.51
65.59 439.66
40.89 471.99
39.35 479.81
78.92 434.78
61.87 446.58
58.33 437.76
39.72 459.36
44.71 462.28
43.48 464.33
46.21 444.36
59.39 438.64
34.03 470.49
41.1 455.13
66.93 450.22
63.73 440.43
42.85 482.98
50.88 460.44
54.2 444.97
68.67 433.94
73.18 439.73
73.88 434.48
60.84 442.33
45.09 457.67
57.76 454.66
67.25 432.21
43.77 457.66
63.76 435.21
47.43 448.22
41.66 475.51
62.91 446.53
57.32 441.3
69.34 433.54
39.04 472.52
44.78 474.77
69.05 435.1
59.8 450.74
65.06 442.7
68.14 426.56
42.32 463.71
66.93 447.06
57.76 452.27
63.94 445.78
68.3 438.65
40.77 480.15
62.52 447.19
48.41 443.04
39.9 488.81
57.76 455.75
49.39 455.86
46.97 457.68
40.05 479.11
74.16 432.84
62.52 448.37
47.45 447.06
49.21 443.53
61.45 445.21
66.51 441.7
66.86 450.93
49.78 451.44
56.89 441.29
44.85 458.85
43.65 481.46
43.41 467.19
41.58 461.54
52.84 439.08
42.74 467.22
44.34 468.8
71.98 426.93
37.73 474.65
44.21 468.97
71.58 433.97
50.16 450.53
59.04 444.51
40.69 469.03
71.14 466.56
52.05 457.57
59.54 440.13
69.84 433.24
43.72 452.55
71.37 443.29
74.99 431.76
44.78 454.97
63.07 456.7
39.9 486.03
39.96 472.79
57.25 452.03
54.2 443.41
67.32 441.93
70.98 432.64
36.24 480.25
39.63 466.68
40.07 494.39
54.42 454.72
56.85 448.71
42.48 469.76
44.89 450.71
58.79 444.01
58.2 453.2
57.85 450.87
63.86 441.73
39.52 465.09
64.63 447.28
39.33 491.16
62.52 450.98
63.56 446.3
79.74 436.48
42.03 460.84
69.51 442.56
41.49 467.3
40.64 479.13
52.3 441.15
59.04 445.52
40.69 475.4
40.69 469.3
41.62 463.57
68.67 445.32
44.21 461.03
43.13 466.74
59.87 444.04
67.25 434.01
44.9 465.23
69.34 440.6
44.84 466.74
75.6 433.48
40.96 473.59
41.74 474.81
44.06 454.75
49.69 452.94
69.13 435.83
39.22 482.19
44.47 466.66
40.12 462.59
64.63 447.82
41.62 462.73
63.21 447.98
39.31 462.72
58.46 442.42
48.41 444.69
39.0 466.7
64.63 453.84
67.32 436.92
36.08 486.37
60.07 440.43
63.07 446.82
39.48 484.91
71.64 437.76
68.08 438.91
39.54 464.19
67.79 442.19
47.43 446.86
44.2 457.15
43.65 482.57
41.26 476.03
72.58 428.89
40.23 472.7
52.3 445.6
52.05 464.78
58.95 440.42
70.79 428.41
70.47 438.5
59.43 438.28
40.64 476.29
58.49 448.46
57.19 438.99
39.22 471.8
42.44 471.81
59.14 449.82
68.08 442.14
58.79 441.46
40.22 477.62
61.87 446.76
39.82 472.52
40.71 471.58
72.39 440.85
77.54 431.37
71.97 437.33
40.71 469.22
40.78 471.11
66.51 439.17
62.26 445.33
39.22 473.71
57.76 452.66
59.43 440.99
38.91 467.42
58.82 444.14
56.53 457.17
54.3 467.87
70.72 442.04
44.58 471.36
39.1 460.7
70.83 431.33
76.86 432.6
59.39 447.61
64.79 443.87
52.3 446.87
41.01 465.74
56.89 447.86
62.96 447.65
63.47 437.87
41.66 483.51
41.46 479.65
58.16 455.16
71.25 431.91
41.5 470.68
69.13 429.28
59.21 450.81
73.5 437.73
44.6 460.21
69.05 442.86
45.0 482.99
65.27 440.0
41.82 478.48
49.82 455.28
66.56 436.94
37.87 461.06
69.45 438.28
39.58 472.61
70.79 426.85
39.72 470.18
54.42 455.38
66.56 428.32
42.49 480.35
56.53 455.56
58.33 447.66
68.67 443.06
58.86 452.43
41.54 477.81
73.77 431.66
73.91 431.8
68.67 446.67
60.29 445.26
69.89 425.72
72.29 430.58
60.27 439.86
59.15 441.11
71.14 434.72
67.45 434.01
41.17 475.64
41.58 460.44
68.67 436.4
40.73 461.03
41.54 479.08
69.14 435.76
45.51 460.14
75.6 442.2
50.78 447.69
73.67 431.15
63.56 445.0
73.21 431.59
44.47 467.22
51.43 445.33
45.09 470.57
39.61 473.77
60.29 447.67
40.05 474.29
71.32 437.14
69.05 432.56
41.79 459.14
60.07 446.19
71.77 428.1
44.47 468.46
66.75 435.02
48.6 445.52
40.55 462.69
61.27 455.75
40.0 463.74
69.68 439.79
58.95 443.26
69.13 432.04
43.96 465.86
45.87 465.6
25.36 469.43
49.3 440.75
38.91 481.32
40.56 479.87
39.16 458.59
71.97 438.62
59.44 445.59
43.56 481.87
41.5 475.01
48.41 436.54
40.66 456.63
62.52 451.69
39.59 463.04
67.71 446.1
59.92 438.67
41.4 466.88
48.41 444.6
59.39 440.26
40.96 483.92
41.2 475.19
44.68 479.24
73.68 434.92
65.46 454.16
58.79 447.58
41.26 467.9
69.13 426.29
45.87 447.02
41.79 455.85
40.22 476.46
68.94 437.48
49.21 452.77
39.33 491.54
64.79 438.41
41.93 476.1
36.99 464.58
40.78 467.74
57.17 442.12
57.5 453.34
69.13 425.29
51.43 449.63
45.78 462.88
42.32 464.67
35.57 489.96
38.08 482.38
77.95 437.95
71.98 429.2
46.63 453.34
70.02 442.47
49.69 462.6
40.96 478.79
52.05 456.11
50.16 450.33
69.88 434.83
73.68 433.43
62.96 456.02
40.67 485.23
37.14 473.57
39.58 469.94
49.83 452.07
41.04 475.32
36.24 480.69
48.06 444.01
56.03 465.17
39.82 480.61
41.5 476.04
49.3 441.76
71.98 428.24
67.71 444.77
45.87 463.1
44.6 470.5
72.99 431.0
69.4 430.68
67.17 436.42
49.82 452.33
63.94 440.16
63.76 435.75
44.57 449.74
72.24 430.73
77.17 432.75
47.43 446.79
41.39 486.35
59.8 453.18
50.23 458.31
41.54 480.26
51.3 448.65
49.5 458.41
64.69 435.39
50.16 450.21
43.14 459.59
75.6 445.84
48.78 441.08
37.85 467.33
63.09 444.19
68.27 432.96
47.93 438.09
36.99 467.9
43.67 475.72
34.69 477.51
69.84 435.13
39.61 477.9
44.2 457.26
44.6 467.53
41.58 465.15
40.1 474.28
65.71 444.49
45.09 452.84
77.54 435.38
75.33 433.57
69.71 435.27
39.63 468.49
70.8 433.07
73.56 430.63
65.74 440.74
39.96 474.49
48.6 449.74
63.76 436.73
70.79 434.58
43.13 473.93
79.74 435.99
43.22 466.83
68.24 427.22
63.77 444.07
41.49 469.57
66.51 459.89
40.71 479.59
64.69 440.92
41.46 480.87
66.54 441.9
69.68 430.2
42.86 465.16
44.45 471.32
40.64 485.43
40.07 495.35
58.49 449.12
42.02 480.53
50.66 457.07
69.94 443.67
44.68 477.52
39.64 472.95
39.69 472.54
40.71 469.17
70.04 435.21
40.22 477.78
39.85 475.89
40.23 483.9
39.16 476.2
43.34 462.16
37.85 471.05
41.26 484.71
63.86 446.34
42.28 469.02
72.86 432.12
40.1 467.28
69.98 429.66
45.09 469.49
40.56 485.87
40.81 481.95
40.02 479.03
69.13 434.5
54.3 464.9
63.94 452.71
69.51 429.74
56.65 457.09
72.29 446.77
41.48 460.76
40.83 471.95
46.21 453.29
60.07 441.61
46.18 464.73
43.69 464.68
73.91 430.59
77.95 438.01
41.04 479.08
74.78 436.39
65.46 447.07
39.58 479.91
43.02 489.05
53.82 463.17
42.02 471.26
40.67 480.49
39.42 473.78
58.16 455.5
58.41 446.27
41.06 482.2
59.8 452.48
43.14 464.48
69.89 438.1
63.47 445.6
67.79 442.43
61.25 436.67
41.85 466.56
71.14 457.29
36.25 487.03
52.72 464.93
44.63 466.0
48.79 469.52
70.04 428.88
41.48 474.3
39.31 461.06
39.39 465.57
41.78 467.67
40.71 466.99
39.39 463.72
49.16 443.78
68.28 445.23
40.66 464.43
36.25 484.36
63.07 442.16
39.63 464.11
49.39 462.48
42.49 477.49
65.59 437.04
40.79 457.09
45.01 450.6
45.0 465.78
70.04 427.1
44.63 459.81
47.43 447.36
39.64 488.92
66.49 433.36
39.04 483.35
41.04 469.53
39.82 476.96
58.46 440.75
43.71 462.55
54.2 448.04
50.59 455.24
40.07 494.75
57.32 444.58
35.79 484.82
66.05 442.9
39.33 485.46
49.5 457.81
43.65 481.92
61.02 443.23
39.69 474.29
71.58 430.46
50.66 455.71
62.26 438.34
41.31 485.83
44.06 452.82
68.94 435.04
59.8 451.21
42.74 465.81
44.92 458.42
39.96 470.22
49.39 449.24
44.92 471.43
44.92 473.26
58.49 452.82
70.32 432.69
60.84 444.13
41.92 467.21
48.6 445.98
73.77 436.91
44.9 455.01
66.56 437.11
40.64 477.06
67.71 441.71
40.07 495.76
66.44 445.63
41.62 464.72
68.94 438.03
72.86 434.78
60.32 444.67
61.41 452.24
45.09 450.92
70.4 436.53
71.77 435.53
68.51 440.01
64.45 443.1
71.94 427.49
68.08 436.25
67.79 440.74
63.31 443.54
51.43 459.42
60.23 439.66
44.84 464.15
56.65 459.1
52.36 455.68
45.51 469.08
41.26 478.02
44.06 456.8
44.89 441.13
43.69 463.88
73.67 430.45
65.71 449.18
48.92 447.89
70.04 431.59
52.3 447.5
41.82 475.58
59.8 453.24
63.21 446.4
44.92 476.81
40.46 474.1
57.76 450.71
66.48 433.62
41.66 465.14
59.87 445.18
39.22 474.12
43.79 483.91
40.27 486.68
43.52 464.98
45.87 481.4
39.04 479.2
41.16 463.86
38.25 472.3
58.84 446.51
51.43 437.71
41.1 458.94
67.17 437.91
39.33 490.76
65.06 439.66
44.9 463.27
39.52 473.99
66.49 433.38
53.82 459.01
40.75 471.44
39.28 471.91
44.47 465.15
51.19 446.66
63.76 438.15
51.19 447.14
43.71 472.32
70.72 441.68
72.99 440.04
64.05 444.82
53.16 457.26
72.58 428.83
43.43 449.07
71.94 435.21
44.2 471.03
48.04 465.56
62.96 442.83
41.48 460.3
40.71 474.25
41.82 477.97
40.46 472.16
46.97 456.08
49.82 452.41
43.22 463.71
67.07 433.72
57.76 456.4
48.98 448.43
36.08 481.6
42.18 457.07
49.39 451.0
75.6 440.28
71.32 437.47
67.71 443.57
69.84 426.6
41.5 470.87
39.85 478.37
58.66 453.92
40.56 470.22
72.24 434.54
63.9 442.89
36.24 479.03
43.99 476.06
36.71 473.88
57.25 451.75
56.85 439.2
58.46 439.7
46.18 463.6
52.84 447.47
56.89 447.92
44.63 471.08
72.43 437.55
51.3 448.27
72.39 431.69
48.14 449.09
58.46 448.79
44.92 460.21
41.17 479.28
41.82 483.11
54.2 450.75
66.54 437.97
41.48 459.76
44.9 457.75
40.1 469.33
69.75 433.28
70.02 444.64
44.9 463.1
44.68 460.91
39.04 479.35
59.21 449.23
40.92 474.51
72.99 435.02
70.72 435.45
48.14 452.38
39.3 480.41
39.72 478.96
42.74 468.87
76.2 434.01
44.6 466.36
75.23 435.28
43.02 486.46
40.1 468.19
41.01 468.37
41.39 474.19
74.22 440.32
38.44 485.32
42.86 464.27
36.18 479.25
70.32 430.4
58.62 447.49
64.69 438.23
40.43 492.09
40.75 475.36
54.9 452.56
74.67 427.84
68.08 433.95
70.8 435.27
58.59 454.62
40.56 472.17
63.31 452.42
42.02 472.17
41.44 481.83
49.15 458.78
62.08 447.5
49.25 463.4
41.26 473.57
70.32 433.72
66.44 431.85
77.95 433.47
74.22 432.84
70.94 436.6
41.17 490.23
41.74 477.16
68.31 441.06
70.98 440.86
41.82 477.94
40.8 474.47
43.02 470.67
65.34 447.31
44.88 466.8
71.94 430.91
69.88 434.75
42.86 469.52
59.43 438.9
70.04 429.56
74.33 432.92
49.16 442.87
41.76 466.59
41.14 479.61
44.63 471.08
59.14 433.37
65.48 443.92
59.14 443.5
64.79 439.89
69.59 434.66
41.38 487.57
41.62 464.64
42.32 470.92
63.73 444.39
48.6 442.48
52.08 449.61
69.34 435.02
43.99 458.67
46.18 461.74
62.39 438.31
48.92 462.38
44.2 460.56
59.21 439.22
58.79 444.64
71.25 430.34
71.29 430.46
45.87 456.79
41.23 468.82
44.9 448.51
44.71 470.77
41.14 465.74
66.56 430.21
50.32 449.23
49.15 461.89
61.45 445.72
39.39 466.13
51.19 448.71
41.23 469.25
66.86 450.56
39.64 464.46
41.5 471.13
48.06 461.52
59.15 451.09
79.74 431.51
40.83 469.8
51.43 442.28
48.92 458.67
43.79 462.4
59.8 453.54
62.96 444.38
58.9 440.52
69.14 433.62
45.0 481.96
44.9 452.75
39.42 481.28
66.05 439.03
73.88 435.75
74.16 436.03
58.49 445.6
56.03 462.65
50.05 438.66
50.32 447.32
39.48 484.55
41.01 476.8
39.04 480.34
48.41 440.63
44.6 459.48
40.43 490.78
38.91 483.56
73.18 429.38
59.21 440.27
51.43 445.34
65.27 447.43
69.94 439.91
50.59 459.27
39.61 478.89
41.66 466.7
43.5 463.5
74.33 436.21
63.47 443.94
63.94 439.63
41.54 460.95
59.14 448.69
75.08 444.63
37.83 473.51
39.54 462.56
50.16 451.76
40.43 491.81
68.08 429.52
49.02 437.9
38.73 467.54
64.45 449.97
66.48 436.62
40.55 477.68
63.86 447.26
63.13 439.76
59.39 437.49
58.2 455.14
41.03 485.5
66.93 444.1
70.94 432.33
44.03 471.23
42.34 463.89
51.19 445.54
59.54 446.09
63.86 445.12
59.21 443.31
39.66 484.16
40.69 477.76
71.29 430.28
62.04 446.48
36.66 481.03
47.83 466.07
67.32 447.47
55.5 455.93
40.0 479.62
47.01 455.06
40.46 475.06
56.85 438.89
69.84 432.7
50.9 452.6
46.21 451.75
71.06 430.66
38.91 491.9
74.78 439.82
39.0 460.73
60.95 449.7
59.15 439.42
65.06 439.84
35.57 485.86
40.12 458.1
39.82 479.92
56.03 458.29
40.07 489.45
73.42 434.0
69.13 431.24
47.93 439.5
40.56 467.46
71.58 429.27
58.95 452.1
42.02 472.41
69.05 442.14
49.3 441.0
41.58 463.07
60.84 445.71
39.81 483.16
68.84 440.45
38.06 481.83
40.62 467.6
52.84 450.88
69.13 425.5
54.42 451.87
69.51 428.94
48.6 439.86
73.42 433.44
73.68 438.23
71.32 436.95
40.56 470.19
40.22 484.66
68.27 430.81
73.17 433.37
48.98 453.02
50.9 453.5
41.23 463.09
44.6 464.56
65.46 452.12
40.69 470.9
64.15 450.89
63.76 445.04
63.07 444.72
40.92 460.38
58.33 446.8
44.06 465.05
40.62 484.13
39.81 488.27
49.21 447.09
58.16 452.02
58.96 455.55
41.92 480.99
41.67 467.68
Pressure Power
1024.07 463.26
1020.04 444.37
1012.16 488.56
1010.24 446.48
1009.23 473.9
1012.23 443.67
1014.02 467.35
1019.12 478.42
1021.78 475.98
1015.14 477.5
1008.64 453.02
1014.66 453.99
1011.31 440.29
1012.77 451.28
1009.48 433.99
1015.76 462.19
1022.86 467.54
1022.6 477.2
1023.97 459.85
1015.15 464.3
1009.09 468.27
1019.16 495.24
1008.52 483.8
1014.3 443.61
1003.18 436.06
1009.97 443.25
1011.11 464.16
1023.57 475.52
1012.14 484.41
1012.69 437.89
1019.02 445.11
1013.64 438.86
1011.11 440.98
1010.08 436.65
1018.76 444.26
1007.29 465.86
1011.4 444.37
1010.08 450.69
1014.69 469.02
1012.04 448.86
1007.62 447.14
1017.24 469.18
1018.33 482.8
1014.12 476.7
1020.63 474.99
1019.28 444.22
1020.24 461.33
1010.96 448.06
1014.51 474.6
1029.14 473.05
1010.58 432.06
1018.71 467.41
1011.6 430.12
1014.82 473.62
1012.94 471.81
1010.23 442.99
1014.65 442.77
1010.18 491.49
1013.68 447.46
1002.25 446.11
1007.03 442.44
1013.61 446.22
1016.67 471.49
1008.89 463.5
1016.02 440.01
1014.56 441.03
1019.49 452.68
1020.43 474.91
1018.71 478.77
998.14 434.2
1017.83 437.91
1024.61 477.61
1016.65 431.65
998.58 430.57
1008.82 481.09
1009.56 445.56
1012.71 475.74
1010.36 435.12
1017.39 446.15
1001.31 436.64
1013.89 436.69
1016.53 468.75
1012.18 466.6
1024.42 465.48
1014.93 441.34
1012.53 441.83
1019.0 464.7
1009.6 437.99
1015.55 459.12
1006.56 429.69
1010.57 459.8
1009.81 433.63
1014.62 442.84
1014.49 485.13
1025.09 459.12
1012.05 445.31
1022.7 480.8
1005.23 432.55
1013.42 443.86
1018.3 449.77
1017.19 470.71
1011.93 452.17
1021.6 478.29
1006.96 428.54
1020.66 478.27
1007.63 439.58
1005.53 457.32
1018.79 475.51
1010.85 439.66
1011.03 471.99
1015.1 479.81
1010.83 434.78
1011.18 446.58
1013.92 437.76
1001.24 459.36
1016.99 462.28
1016.08 464.33
1010.71 444.36
1014.32 438.64
1018.69 470.49
1001.86 455.13
1017.06 450.22
1009.34 440.43
1014.02 482.98
1014.19 460.44
1012.81 444.97
1005.2 433.94
1012.28 439.73
1005.89 434.48
1017.93 442.33
1014.26 457.67
1018.8 454.66
1017.71 432.21
1012.25 457.66
1010.27 435.21
1007.64 448.22
1013.79 475.51
1013.24 446.53
1011.7 441.3
1007.67 433.54
1020.45 472.52
1012.59 474.77
1001.62 435.1
1016.92 450.74
1014.32 442.7
1003.34 426.56
1016.0 463.71
1016.85 447.06
1018.02 452.27
1018.49 445.78
1017.93 438.65
1011.55 480.15
1016.46 447.19
1008.47 443.04
1008.06 488.81
1016.26 455.75
1018.83 455.86
1013.94 457.68
1014.95 479.11
1007.44 432.84
1016.18 448.37
1007.56 447.06
1014.1 443.53
1011.13 445.21
1015.53 441.7
1013.05 450.93
1002.95 451.44
1012.32 441.29
1014.48 458.85
1018.24 481.46
1016.93 467.19
1020.5 461.54
1006.28 439.08
1028.79 467.22
1019.49 468.8
1004.66 426.93
1024.36 474.65
1022.93 468.97
1010.18 433.97
1009.52 450.53
1011.98 444.51
1015.29 469.03
1019.36 466.56
1012.15 457.57
1006.24 440.13
1003.57 433.24
1008.64 452.55
1002.04 443.29
1005.47 431.76
1007.81 454.97
1012.42 456.7
1007.75 486.03
1011.37 472.79
1010.12 452.03
1012.26 443.41
1014.49 441.93
1007.51 432.64
1013.15 480.25
1004.47 466.68
1020.19 494.39
1012.46 454.72
1012.28 448.71
1013.43 469.76
1009.64 450.71
1009.8 444.01
1017.46 453.2
1012.39 450.87
1019.67 441.73
1018.41 465.09
1020.59 447.28
1011.54 491.16
1017.99 450.98
1013.75 446.3
1008.37 436.48
1017.41 460.84
1013.43 442.56
1020.19 467.3
1021.47 479.13
1008.72 441.15
1011.78 445.52
1015.62 475.4
1014.91 469.3
1017.17 463.57
1006.71 445.32
1020.36 461.03
1014.99 466.74
1018.47 444.04
1017.6 434.01
1020.5 465.23
1009.63 440.6
1023.66 466.74
1017.43 433.48
1023.36 473.59
1020.75 474.81
1017.58 454.75
1009.6 452.94
1009.94 435.83
1014.53 482.19
1030.46 466.66
1013.03 462.59
1020.69 447.82
1014.55 462.73
1012.06 447.98
1009.15 462.72
1016.82 442.42
1008.64 444.69
1016.73 466.7
1020.38 453.84
1013.83 436.92
1021.82 486.37
1015.42 440.43
1010.94 446.82
1005.11 484.91
1008.27 437.76
1013.27 438.91
1007.97 464.19
1009.89 442.19
1008.38 446.86
1018.89 457.15
1020.14 482.57
1007.44 476.03
1008.69 428.89
1018.07 472.7
1009.04 445.6
1014.63 464.78
1017.02 440.42
1003.96 428.41
1010.65 438.5
1007.84 438.28
1022.35 476.29
1011.5 448.46
1008.62 438.99
1017.9 471.8
1012.74 471.81
1016.12 449.82
1013.13 442.14
1009.74 441.46
1011.37 477.62
1011.45 446.76
1012.46 472.52
1021.27 471.58
1001.15 440.85
1011.33 431.37
1008.64 437.33
1015.68 469.22
1023.51 471.11
1010.98 439.17
1012.11 445.33
1018.62 473.71
1016.28 452.66
1007.12 440.99
1014.48 467.42
1010.02 444.14
1020.57 457.17
1015.92 467.87
1009.78 442.04
1019.52 471.36
1009.81 460.7
1010.35 431.33
998.59 432.6
1014.07 447.61
1016.27 443.87
1009.2 446.87
1020.57 465.74
1014.02 447.86
1020.16 447.65
1011.78 437.87
1016.87 483.51
1018.21 479.65
1016.88 455.16
1002.49 431.91
1014.13 470.68
1009.29 429.28
1018.32 450.81
1011.49 437.73
1015.16 460.21
1001.6 442.86
1021.51 482.99
1013.27 440.0
1033.25 478.48
1015.01 455.28
1002.07 436.94
1022.36 461.06
1013.97 438.28
1011.81 472.61
1003.7 426.85
1017.76 470.18
1012.31 455.38
1006.44 428.32
1010.57 480.35
1020.2 455.56
1013.14 447.66
1006.74 443.06
1014.19 452.43
1019.94 477.81
1004.72 431.66
1004.53 431.8
1006.65 446.67
1018.0 445.26
1013.85 425.72
1008.73 430.58
1018.94 439.86
1013.31 441.11
1011.6 434.72
1014.23 434.01
1019.43 475.64
1020.43 460.44
1005.46 436.4
1018.7 461.03
1019.94 479.08
1009.31 435.76
1015.22 460.14
1017.37 442.2
1008.83 447.69
1006.65 431.15
1014.32 445.0
1001.32 431.59
1027.94 467.22
1012.16 445.33
1013.21 470.57
1018.72 473.77
1017.42 447.67
1014.78 474.29
1008.07 437.14
1003.12 432.56
1009.72 459.14
1016.03 446.19
1006.38 428.1
1030.18 468.46
1017.95 435.02
1002.38 445.52
1003.36 462.69
1019.26 455.75
1015.89 463.74
1011.95 439.79
1016.99 443.26
1009.3 432.04
1013.32 465.86
1009.05 465.6
1009.35 469.43
1003.4 440.75
1015.82 481.32
1022.64 479.87
1005.7 458.59
1009.62 438.62
1012.38 445.59
1015.13 481.87
1013.58 475.01
1008.53 436.54
1016.28 456.63
1015.63 451.69
1010.93 463.04
1007.68 446.1
1009.94 438.67
1019.7 466.88
1008.42 444.6
1015.4 440.26
1023.28 483.92
1017.18 475.19
1023.06 479.24
1014.95 434.92
1014.0 454.16
1012.42 447.58
1021.67 467.9
1010.27 426.29
1007.8 447.02
1005.47 455.85
1010.31 476.46
1007.53 437.48
1014.61 452.77
1012.57 491.54
1017.22 438.41
1019.81 476.1
1007.87 464.58
1023.91 467.74
1010.0 442.12
1014.53 453.34
1010.44 425.29
1011.74 449.63
1025.27 462.88
1015.71 464.67
1027.17 489.96
1020.27 482.38
1009.45 437.95
1004.74 429.2
1013.03 453.34
1010.58 442.47
1015.14 462.6
1024.57 478.79
1012.34 456.11
1005.81 450.33
1007.21 434.83
1015.1 433.43
1020.76 456.02
1018.08 485.23
1013.03 473.57
1011.17 469.94
1008.69 452.07
1021.82 475.32
1013.39 480.69
1013.12 444.01
1020.41 465.17
1012.87 480.61
1013.39 476.04
1003.51 441.76
1005.19 428.24
1004.0 444.77
1008.58 463.1
1018.19 470.5
1007.04 431.0
1004.27 430.68
1006.6 436.42
1016.19 452.33
1010.64 440.16
1010.18 435.75
1008.48 449.74
1010.74 430.73
1009.55 432.75
1007.88 446.79
1018.12 486.35
1015.66 453.18
1015.73 458.31
1019.7 480.26
1011.89 448.65
1012.67 458.41
1006.37 435.39
1010.49 450.21
1018.68 459.59
1017.19 445.84
1018.17 441.08
1009.89 467.33
1016.56 444.19
1007.96 432.96
1002.85 438.09
1006.86 467.9
1012.68 475.72
1027.72 477.51
1006.37 435.13
1017.99 477.9
1019.18 457.26
1015.88 467.53
1021.08 465.15
1014.42 474.28
1013.85 444.49
1014.15 452.84
1008.5 435.38
1003.88 433.57
1009.04 435.27
1005.35 468.49
1009.9 433.07
1004.85 430.63
1013.29 440.74
1026.31 474.49
1005.72 449.74
1010.09 436.73
1006.53 434.58
1017.24 473.93
1007.03 435.99
1009.45 466.83
1005.29 427.22
1013.39 444.07
1020.11 469.57
1015.18 459.89
1024.91 479.59
1007.21 440.92
1020.45 480.87
1009.93 441.9
1011.35 430.2
1014.62 465.16
1021.19 471.32
1020.91 485.43
1012.27 495.35
1010.85 449.12
1006.22 480.53
1014.89 457.07
1010.7 443.67
1023.44 477.52
1012.52 472.95
1003.92 472.54
1015.85 469.17
1011.09 435.21
1004.81 477.78
1012.86 475.89
1017.75 483.9
1016.53 476.2
1015.47 462.16
1011.24 471.05
1010.6 484.71
1015.43 446.34
1007.21 469.02
1004.23 432.12
1015.51 467.28
1013.29 429.66
1013.16 469.49
1023.23 485.87
1026.0 481.95
1031.1 479.03
1010.99 434.5
1015.16 464.9
1020.02 452.71
1010.84 429.74
1020.67 457.09
1011.61 446.77
1014.46 460.76
1008.31 471.95
1014.09 453.29
1016.34 441.61
1017.01 464.73
1016.91 464.68
1003.72 430.59
1014.19 438.01
1021.84 479.08
1009.28 436.39
1016.25 447.07
1011.9 479.91
1013.88 489.05
1016.46 463.17
1001.18 471.26
1011.64 480.49
1025.41 473.78
1016.76 455.5
1013.78 446.27
1021.21 482.2
1016.72 452.48
1011.92 464.48
1015.29 438.1
1012.77 445.6
1010.37 442.43
1011.56 436.67
1016.54 466.56
1019.65 457.29
1029.65 487.03
1026.45 464.93
1019.28 466.0
1017.44 469.52
1011.18 428.88
1018.49 474.3
1009.69 461.06
1014.09 465.57
1012.3 467.67
1016.02 466.99
1013.73 463.72
1004.03 443.78
1005.43 445.23
1017.13 464.43
1028.31 484.36
1012.5 442.16
1004.64 464.11
1018.35 462.48
1009.59 477.49
1012.78 437.04
1003.8 457.09
1012.22 450.6
1023.25 465.78
1010.15 427.1
1020.14 459.81
1006.64 447.36
1011.0 488.92
1012.96 433.36
1021.99 483.35
1026.57 469.53
1012.27 476.96
1017.5 440.75
1024.51 462.55
1012.05 448.04
1016.22 455.24
1011.8 494.75
1012.55 444.58
1011.56 484.82
1019.6 442.9
1009.68 485.46
1012.82 457.81
1013.85 481.92
1009.63 443.23
1000.91 474.29
1009.98 430.46
1013.56 455.71
1011.25 438.34
1003.24 485.83
1017.76 452.82
1007.68 435.04
1016.82 451.21
1028.41 465.81
1025.04 458.42
1026.09 470.22
1020.84 449.24
1023.84 471.43
1023.74 473.26
1011.7 452.82
1008.1 432.69
1017.91 444.13
1029.8 467.21
1002.33 445.98
1002.42 436.91
1009.05 455.01
1002.47 437.11
1020.68 477.06
1006.65 441.71
1019.63 495.76
1011.33 445.63
1012.88 464.72
1005.94 438.03
1003.47 434.78
1015.63 444.67
1012.2 452.24
1014.19 450.92
1006.65 436.53
1005.75 435.53
1013.23 440.01
1008.72 443.1
1007.18 427.49
1012.99 436.25
1009.99 440.74
1015.02 443.54
1010.82 459.42
1009.76 439.66
1023.55 464.15
1020.55 459.1
1014.76 455.68
1015.33 469.08
1007.71 478.02
1017.36 456.8
1009.18 441.13
1017.05 463.88
1006.14 430.45
1014.24 449.18
1010.92 447.89
1010.4 431.59
1009.36 447.5
1033.04 475.58
1016.77 453.24
1012.59 446.4
1025.1 476.81
1019.29 474.1
1016.66 450.71
1006.4 433.62
1011.45 465.14
1019.08 445.18
1015.3 474.12
1016.08 483.91
1010.55 486.68
1022.43 464.98
1010.83 481.4
1021.81 479.2
1005.85 463.86
1012.76 472.3
1001.31 446.51
1005.93 437.71
1001.96 458.94
1007.62 437.91
1009.96 490.76
1013.4 439.66
1007.58 463.27
1016.68 473.99
1012.83 433.38
1015.13 459.01
1016.05 471.44
1012.97 471.91
1028.2 465.15
1008.25 446.66
1009.78 438.15
1008.81 447.14
1025.53 472.32
1010.16 441.68
1009.33 440.04
1009.82 444.82
1014.5 457.26
1009.13 428.83
1009.93 449.07
1009.38 435.21
1017.59 471.03
1012.47 465.56
1019.86 442.83
1017.26 460.3
1023.07 474.25
1033.3 477.97
1019.1 472.16
1014.22 456.08
1014.9 452.41
1011.31 463.71
1006.26 433.72
1016.0 456.4
1015.41 448.43
1020.63 481.6
1001.16 457.07
1019.8 451.0
1018.48 440.28
1002.26 437.47
1004.07 443.57
1004.91 426.6
1013.12 470.87
1012.9 478.37
1013.32 453.92
1020.79 470.22
1011.37 434.54
1013.11 442.89
1013.29 479.03
1020.5 476.06
1022.62 473.88
1010.84 451.75
1012.68 439.2
1015.58 439.7
1013.68 463.6
1004.21 447.47
1013.23 447.92
1020.44 471.08
1007.99 437.55
1012.36 448.27
998.47 431.69
1016.57 449.09
1015.93 448.79
1025.21 460.21
1013.54 479.28
1032.67 483.11
1011.46 450.75
1010.43 437.97
1008.53 459.76
1020.5 457.75
1015.48 469.33
1009.74 433.28
1010.23 444.64
1021.3 463.1
1022.01 460.91
1023.95 479.35
1017.65 449.23
1021.83 474.51
1007.81 435.02
1009.43 435.45
1013.3 452.38
1019.73 480.41
1019.54 478.96
1026.58 468.87
1007.89 434.01
1013.85 466.36
1011.44 435.28
1014.51 486.46
1015.51 468.19
1022.14 468.37
1019.17 474.19
1009.52 440.32
1015.35 485.32
1014.38 464.27
1013.66 479.25
1007.0 430.4
1016.65 447.49
1006.85 438.23
1025.46 492.09
1015.13 475.36
1016.68 452.56
1015.98 427.84
1010.8 433.95
1008.48 435.27
1014.04 454.62
1020.36 472.17
1015.96 452.42
1003.19 472.17
1018.01 481.83
1021.83 458.78
1022.47 447.5
1019.04 463.4
1022.67 473.57
1009.07 433.72
1011.2 431.85
1012.13 433.47
1007.45 432.84
1007.29 436.6
1020.12 490.23
1020.58 477.16
1010.44 441.06
1007.22 440.86
1033.08 477.94
1026.56 474.47
1012.18 470.67
1013.7 447.31
1018.14 466.8
1007.4 430.91
1007.2 434.75
1010.82 469.52
1008.88 438.9
1010.51 429.56
1013.53 432.92
1005.68 442.87
1022.57 466.59
1028.04 479.61
1019.12 471.08
1016.51 433.37
1018.8 443.92
1016.74 443.5
1017.37 439.89
1008.9 434.66
1021.95 487.57
1013.76 464.64
1017.26 470.92
1014.37 444.39
1002.54 442.48
1005.25 449.61
1009.43 435.02
1021.81 458.67
1016.63 461.74
1008.09 438.31
1011.68 462.38
1019.39 460.56
1013.37 439.22
1009.71 444.64
999.8 430.34
1008.37 430.46
1009.02 456.79
994.17 468.82
1008.79 448.51
1014.67 470.77
1025.79 465.74
1005.31 430.21
1008.62 449.23
1021.91 461.89
1010.97 445.72
1013.36 466.13
1008.38 448.71
998.43 469.25
1013.04 450.56
1008.94 464.46
1014.87 471.13
1010.92 461.52
1012.04 451.09
1005.43 431.51
1009.65 469.8
1012.05 442.28
1011.84 458.67
1016.13 462.4
1015.18 453.54
1019.81 444.38
1003.39 440.52
1007.68 433.62
1023.68 481.96
1008.89 452.75
1026.4 481.28
1020.28 439.03
1005.64 435.75
1009.72 436.03
1011.03 445.6
1020.27 462.65
1005.87 438.66
1008.54 447.32
1004.85 484.55
1024.9 476.8
1023.99 480.34
1010.53 440.63
1014.27 459.48
1025.98 490.78
1019.25 483.56
1012.26 429.38
1013.49 440.27
1011.34 445.34
1013.86 447.43
1004.37 439.91
1016.11 459.27
1017.88 478.89
1012.41 466.7
1021.39 463.5
1015.04 436.21
1011.95 443.94
1012.87 439.63
1013.21 460.95
1015.99 448.69
1006.24 444.63
1005.49 473.51
1008.56 462.56
1011.07 451.76
1025.68 491.81
1011.04 429.52
1007.59 437.9
1003.18 467.54
1015.35 449.97
1003.61 436.62
1023.37 477.68
1016.04 447.26
1011.8 439.76
1015.23 437.49
1018.29 455.14
1021.76 485.5
1016.81 444.1
1006.91 432.33
1008.87 471.23
1017.93 463.89
1009.2 445.54
1007.99 446.09
1017.82 445.12
1018.29 443.31
1015.14 484.16
1019.86 477.76
1008.36 430.28
1010.39 446.48
1028.11 481.03
1007.41 466.07
1013.2 447.47
1019.83 455.93
1021.15 479.62
1014.28 455.06
1019.87 475.06
1012.59 438.89
1003.38 432.7
1011.89 452.6
1010.46 451.75
1008.16 430.66
1019.04 491.9
1010.04 439.82
1015.91 460.73
1015.14 449.7
1013.88 439.42
1013.33 439.84
1025.58 485.86
1011.81 458.1
1012.89 479.92
1019.94 458.29
1017.29 489.45
1012.17 434.0
1010.69 431.24
1003.26 439.5
1019.48 467.46
1010.0 429.27
1016.95 452.1
999.83 472.41
1002.75 442.14
1003.56 441.0
1020.76 463.07
1017.99 445.71
1017.11 483.16
1010.75 440.45
1020.6 481.83
1015.53 467.6
1004.29 450.88
1001.22 425.5
1013.95 451.87
1010.51 428.94
1002.59 439.86
1011.21 433.44
1015.12 438.23
1007.68 436.95
1021.67 470.19
1011.6 484.66
1007.56 430.81
1010.05 433.37
1014.17 453.02
1012.6 453.5
995.88 463.09
1016.25 464.56
1017.22 452.12
1015.66 470.9
1021.08 450.89
1009.85 445.04
1011.49 444.72
1022.07 460.38
1013.05 446.8
1018.34 465.05
1016.55 484.13
1017.01 488.27
1013.85 447.09
1017.16 452.02
1014.16 455.55
1029.41 480.99
1012.96 467.68
Humidity Power
73.17 463.26
59.08 444.37
92.14 488.56
76.64 446.48
96.62 473.9
58.77 443.67
75.24 467.35
66.43 478.42
41.25 475.98
70.72 477.5
75.04 453.02
64.22 453.99
84.15 440.29
61.83 451.28
87.59 433.99
43.08 462.19
48.84 467.54
77.51 477.2
63.59 459.85
55.28 464.3
66.26 468.27
64.77 495.24
83.31 483.8
47.19 443.61
54.93 436.06
74.62 443.25
72.52 464.16
88.44 475.52
92.28 484.41
41.85 437.89
44.28 445.11
64.58 438.86
63.25 440.98
78.61 436.65
44.51 444.26
89.46 465.86
74.52 444.37
88.86 450.69
75.51 469.02
78.64 448.86
76.65 447.14
80.44 469.18
79.89 482.8
88.28 476.7
84.6 474.99
42.69 444.22
78.41 461.33
61.07 448.06
50.0 474.6
77.29 473.05
43.66 432.06
83.8 467.41
66.47 430.12
93.09 473.62
80.52 471.81
68.99 442.99
57.27 442.77
95.53 491.49
71.72 447.46
57.88 446.11
63.34 442.44
48.07 446.22
91.87 471.49
87.27 463.5
64.4 440.01
43.4 441.03
72.24 452.68
90.22 474.91
74.0 478.77
71.85 434.2
86.62 437.91
97.41 477.61
84.44 431.65
81.55 430.57
75.66 481.09
79.41 445.56
58.91 475.74
90.06 435.12
79.0 446.15
69.47 436.64
51.47 436.69
83.13 468.75
40.33 466.6
81.69 465.48
94.55 441.34
91.81 441.83
63.62 464.7
49.35 437.99
69.61 459.12
38.75 429.69
90.17 459.8
81.24 433.63
48.46 442.84
76.72 485.13
51.16 459.12
76.34 445.31
67.3 480.8
52.38 432.55
76.44 443.86
91.55 449.77
71.9 470.71
80.05 452.17
63.77 478.29
62.26 428.54
89.04 478.27
58.02 439.58
81.82 457.32
91.14 475.51
88.92 439.66
84.83 471.99
91.76 479.81
86.56 434.78
57.21 446.58
54.25 437.76
63.8 459.36
33.71 462.28
67.25 464.33
60.11 444.36
74.55 438.64
67.34 470.49
42.75 455.13
55.2 450.22
83.61 440.43
88.78 482.98
100.12 460.44
64.52 444.97
51.41 433.94
85.78 439.73
75.41 434.48
81.63 442.33
51.92 457.67
70.12 454.66
53.83 432.21
77.23 457.66
65.67 435.21
71.18 448.22
81.96 475.51
79.54 446.53
47.09 441.3
57.69 433.54
78.89 472.52
85.29 474.77
40.13 435.1
77.06 450.74
67.38 442.7
62.44 426.56
77.43 463.71
58.77 447.06
67.72 452.27
42.14 445.78
84.16 438.65
89.79 480.15
67.21 447.19
72.14 443.04
97.49 488.81
87.74 455.75
96.3 455.86
61.25 457.68
88.38 479.11
74.77 432.84
68.18 448.37
77.2 447.06
49.54 443.53
92.22 445.21
33.65 441.7
64.59 450.93
100.09 451.44
68.04 441.29
48.94 458.85
74.47 481.46
81.02 467.19
71.17 461.54
53.85 439.08
70.67 467.22
59.36 468.8
57.17 426.93
70.29 474.65
83.37 468.97
87.36 433.97
100.09 450.53
68.78 444.51
70.98 469.03
75.68 466.56
47.49 457.57
71.99 440.13
66.55 433.24
74.73 452.55
64.78 443.29
75.13 431.76
56.38 454.97
94.35 456.7
86.55 486.03
82.95 472.79
88.42 452.03
85.61 443.41
58.39 441.93
74.28 432.64
87.85 480.25
83.5 466.68
65.24 494.39
75.01 454.72
84.52 448.71
80.52 469.76
75.14 450.71
75.75 444.01
76.72 453.2
85.47 450.87
57.95 441.73
78.32 465.09
52.2 447.28
93.69 491.16
75.74 450.98
67.56 446.3
69.46 436.48
74.58 460.84
53.23 442.56
88.72 467.3
96.16 479.13
68.26 441.15
86.39 445.52
85.34 475.4
72.64 469.3
97.82 463.57
77.22 445.32
80.59 461.03
46.91 466.74
57.76 444.04
53.09 434.01
84.31 465.23
71.58 440.6
92.97 466.74
74.55 433.48
78.96 473.59
64.44 474.81
68.23 454.75
70.81 452.94
61.66 435.83
77.76 482.19
69.49 466.66
96.26 462.59
55.74 447.82
95.61 462.73
84.75 447.98
75.3 462.72
67.5 442.42
80.92 444.69
79.23 466.7
81.1 453.84
32.8 436.92
84.31 486.37
46.15 440.43
53.96 446.82
59.83 484.91
75.3 437.76
42.53 438.91
70.58 464.19
91.69 442.19
63.55 446.86
61.51 457.15
69.55 482.57
98.08 476.03
79.34 428.89
81.28 472.7
78.99 445.6
80.38 464.78
51.16 440.42
72.17 428.41
75.39 438.5
68.91 438.28
96.38 476.29
70.54 448.46
45.8 438.99
57.95 471.8
81.89 471.81
69.32 449.82
59.14 442.14
81.54 441.46
85.81 477.62
65.41 446.76
81.15 472.52
95.87 471.58
90.24 440.85
75.13 431.37
88.22 437.33
81.48 469.22
89.84 471.11
43.57 439.17
63.16 445.33
57.14 473.71
77.76 452.66
90.56 440.99
60.98 467.42
70.31 444.14
74.05 457.17
75.42 467.87
82.25 442.04
67.95 471.36
100.09 460.7
47.28 431.33
72.41 432.6
77.67 447.61
63.7 443.87
79.77 446.87
93.84 465.74
84.95 447.86
70.16 447.65
84.24 437.87
73.32 483.51
86.17 479.65
65.43 455.16
94.59 431.91
86.8 470.68
58.18 429.28
89.66 450.81
87.39 437.73
36.35 460.21
79.62 442.86
50.52 482.99
51.96 440.0
74.73 478.48
78.33 455.28
85.19 436.94
83.13 461.06
53.49 438.28
88.86 472.61
60.89 426.85
61.14 470.18
68.29 455.38
57.62 428.32
83.63 480.35
78.1 455.56
66.34 447.66
79.02 443.06
68.96 452.43
71.13 477.81
87.01 431.66
74.3 431.8
77.62 446.67
59.56 445.26
41.66 425.72
73.27 430.58
77.16 439.86
67.02 441.11
52.8 434.72
39.04 434.01
65.47 475.64
74.32 460.44
69.22 436.4
93.88 461.03
69.83 479.08
84.11 435.76
78.65 460.14
69.31 442.2
70.3 447.69
68.23 431.15
71.76 445.0
85.88 431.59
71.09 467.22
52.67 445.33
89.68 470.57
73.66 473.77
58.94 447.67
87.05 474.29
67.0 437.14
43.18 432.56
80.62 459.14
59.72 446.19
72.1 428.1
69.15 468.46
55.66 435.02
61.19 445.52
74.62 462.69
73.35 455.75
68.85 463.74
39.89 439.79
53.16 443.26
52.97 432.04
79.87 465.86
84.09 465.6
100.15 469.43
79.77 440.75
88.99 481.32
76.14 479.87
69.13 458.59
93.03 438.62
77.92 445.59
74.89 481.87
88.7 475.01
62.94 436.54
89.62 456.63
81.04 451.69
94.53 463.04
64.02 446.1
70.57 438.67
70.32 466.88
84.86 444.6
81.41 440.26
89.45 483.92
82.71 475.19
93.93 479.24
70.6 434.92
87.68 454.16
87.58 447.58
74.4 467.9
67.35 426.29
63.61 447.02
76.89 455.85
78.08 476.46
69.17 437.48
53.31 452.77
93.32 491.54
42.47 438.41
82.58 476.1
94.59 464.58
86.31 467.74
72.57 442.12
80.76 453.34
71.93 425.29
47.54 449.63
95.72 462.88
77.03 464.67
80.49 489.96
77.67 482.38
78.72 437.95
58.77 429.2
74.8 453.34
51.34 442.47
90.41 462.6
91.1 478.79
62.57 456.11
84.27 450.33
42.93 434.83
40.96 433.43
76.53 456.02
69.74 485.23
74.99 473.57
70.45 469.94
91.49 452.07
88.97 475.32
89.13 480.69
46.52 444.01
60.55 465.17
88.71 480.61
89.15 476.04
83.02 441.76
75.19 428.24
87.35 444.77
85.66 463.1
91.66 470.5
63.47 431.0
72.25 430.68
70.58 436.42
60.1 452.33
89.29 440.16
67.43 435.75
67.58 449.74
70.8 430.73
63.62 432.75
66.68 446.79
90.76 486.35
75.34 453.18
59.77 458.31
80.79 480.26
74.1 448.65
41.34 458.41
58.78 435.39
97.78 450.21
74.85 459.59
69.84 445.84
75.36 441.08
85.8 467.33
90.11 444.19
61.63 432.96
44.76 438.09
89.7 467.9
72.51 475.72
74.98 477.51
79.59 435.13
78.42 477.9
61.23 457.26
47.56 467.53
93.06 465.15
89.65 474.28
50.5 444.49
44.84 452.84
85.32 435.38
82.94 433.57
67.26 435.27
79.05 468.49
62.03 433.07
94.36 430.63
60.02 440.74
95.46 474.49
84.92 449.74
62.8 436.73
90.81 434.58
80.9 473.93
55.84 435.99
75.3 466.83
37.34 427.22
79.5 444.07
87.29 469.57
81.5 459.89
76.42 479.59
75.75 440.92
84.95 480.87
62.37 441.9
49.25 430.2
74.16 465.16
90.55 471.32
94.28 485.43
63.31 495.35
78.9 449.12
90.97 480.53
87.34 457.07
80.8 443.67
90.95 477.52
69.97 472.95
89.45 472.54
76.08 469.17
83.35 435.21
92.16 477.78
58.42 475.89
85.06 483.9
88.91 476.2
83.33 462.16
88.49 471.05
96.88 484.71
73.86 446.34
65.17 469.02
69.41 432.12
81.23 467.28
54.07 429.66
89.17 469.49
78.85 485.87
84.44 481.95
83.02 479.03
90.66 434.5
75.29 464.9
82.6 452.71
45.4 429.74
66.33 457.09
45.33 446.77
67.12 460.76
84.14 471.95
80.81 453.29
49.13 441.61
87.29 464.73
52.95 464.68
68.92 430.59
85.21 438.01
88.56 479.08
55.09 436.39
48.64 447.07
87.85 479.91
87.42 489.05
62.75 463.17
94.86 471.26
63.54 480.49
69.46 473.78
74.66 455.5
80.57 446.27
84.7 482.2
72.6 452.48
52.63 464.48
82.01 438.1
75.22 445.6
51.05 442.43
80.1 436.67
81.58 466.56
65.94 457.29
86.74 487.03
62.57 464.93
57.37 466.0
88.91 469.52
72.26 428.88
74.98 474.3
71.19 461.06
62.82 465.57
55.31 467.67
71.57 466.99
59.16 463.72
40.8 443.78
67.63 445.23
97.2 464.43
91.16 484.36
64.81 442.16
85.61 464.11
93.42 462.48
77.36 477.49
67.03 437.04
89.45 457.09
54.84 450.6
53.48 465.78
54.47 427.1
43.36 459.81
48.92 447.36
81.22 488.92
60.35 433.36
75.98 483.35
74.24 469.53
85.21 476.96
68.46 440.75
78.31 462.55
89.25 448.04
68.57 455.24
67.38 494.75
53.6 444.58
91.69 484.82
78.21 442.9
94.19 485.46
37.19 457.81
83.53 481.92
79.45 443.23
99.9 474.29
50.39 430.46
74.33 455.71
83.66 438.34
89.48 485.83
64.59 452.82
75.68 435.04
64.18 451.21
70.09 465.81
70.58 458.42
99.28 470.22
81.89 449.24
87.99 471.43
88.21 473.26
91.29 452.82
52.72 432.69
67.5 444.13
92.05 467.21
63.23 445.98
90.88 436.91
74.91 455.01
85.39 437.11
96.98 477.06
56.28 441.71
65.62 495.76
55.32 445.63
88.88 464.72
39.49 438.03
54.59 434.78
57.19 444.67
45.06 452.24
40.62 450.92
90.21 436.53
90.91 435.53
74.96 440.01
54.21 443.1
63.62 427.49
50.04 436.25
51.23 440.74
82.71 443.54
92.04 459.42
90.67 439.66
91.14 464.15
70.43 459.1
66.63 455.68
86.95 469.08
96.69 478.02
70.88 456.8
47.14 441.13
63.36 463.88
60.58 430.45
54.3 449.18
65.09 447.89
48.16 431.59
81.51 447.5
68.57 475.58
73.16 453.24
80.88 446.4
85.4 476.81
75.77 474.1
75.76 450.71
70.21 433.62
55.53 465.14
80.48 445.18
72.41 474.12
83.25 483.91
82.12 486.68
94.75 464.98
95.79 481.4
86.02 479.2
78.29 463.86
82.23 472.3
52.86 446.51
60.66 437.71
62.77 458.94
65.54 437.91
95.4 490.76
51.78 439.66
63.62 463.27
83.09 473.99
61.81 433.38
68.24 459.01
72.41 471.44
79.64 471.91
66.95 465.15
91.98 446.66
64.96 438.15
88.93 447.14
85.62 472.32
84.0 441.68
89.41 440.04
67.4 444.82
76.75 457.26
89.06 428.83
64.02 449.07
64.12 435.21
81.22 471.03
100.13 465.56
58.07 442.83
63.42 460.3
83.32 474.25
74.28 477.97
71.91 472.16
85.8 456.08
55.58 452.41
69.7 463.71
63.79 433.72
86.59 456.4
48.28 448.43
80.42 481.6
98.58 457.07
72.83 451.0
56.07 440.28
67.13 437.47
84.49 443.57
68.37 426.6
86.07 470.87
83.82 478.37
74.86 453.92
53.52 470.22
80.61 434.54
43.56 442.89
89.35 479.03
97.28 476.06
80.49 473.88
88.9 451.75
49.7 439.2
68.64 439.7
98.58 463.6
82.12 447.47
78.32 447.92
86.04 471.08
91.36 437.55
81.02 448.27
76.05 431.69
71.81 449.09
82.13 448.79
74.27 460.21
71.32 479.28
74.59 483.11
84.44 450.75
43.39 437.97
87.2 459.76
77.11 457.75
82.81 469.33
85.67 433.28
95.58 444.64
74.46 463.1
90.02 460.91
81.93 479.35
86.29 449.23
85.43 474.51
71.66 435.02
71.33 435.45
67.72 452.38
84.23 480.41
74.44 478.96
71.48 468.87
56.3 434.01
68.13 466.36
68.35 435.28
85.23 486.46
79.78 468.19
98.98 468.37
72.87 474.19
90.93 440.32
72.94 485.32
72.3 464.27
77.74 479.25
78.29 430.4
69.1 447.49
55.79 438.23
75.09 492.09
88.98 475.36
64.26 452.56
25.89 427.84
59.18 433.95
67.48 435.27
89.85 454.62
50.62 472.17
83.97 452.42
96.51 472.17
80.09 481.83
84.02 458.78
61.97 447.5
88.51 463.4
81.83 473.57
90.63 433.72
73.37 431.85
77.5 433.47
57.46 432.84
51.91 436.6
79.14 490.23
69.24 477.16
41.85 441.06
95.1 440.86
74.53 477.94
64.85 474.47
57.07 470.67
62.9 447.31
72.21 466.8
65.99 430.91
73.67 434.75
88.59 469.52
61.19 438.9
49.37 429.56
48.65 432.92
56.18 442.87
71.56 466.59
87.46 479.61
70.02 471.08
61.2 433.37
60.54 443.92
71.82 443.5
44.8 439.89
67.32 434.66
78.77 487.57
96.02 464.64
90.56 470.92
83.19 444.39
68.45 442.48
99.19 449.61
88.11 435.02
79.29 458.67
87.76 461.74
82.56 438.31
79.24 462.38
67.24 460.56
58.98 439.22
84.22 444.64
89.12 430.34
50.07 430.46
98.86 456.79
95.79 468.82
70.06 448.51
41.71 470.77
86.55 465.74
71.97 430.21
96.4 449.23
91.73 461.89
91.62 445.72
59.14 466.13
92.56 448.71
83.71 469.25
55.43 450.56
74.91 464.46
89.41 471.13
69.81 461.52
86.01 451.09
86.05 431.51
80.98 469.8
63.62 442.28
64.16 458.67
75.63 462.4
80.21 453.54
59.7 444.38
47.6 440.52
63.78 433.62
89.37 481.96
70.55 452.75
84.42 481.28
80.62 439.03
52.56 435.75
83.26 436.03
70.64 445.6
89.95 462.65
51.53 438.66
84.83 447.32
59.68 484.55
97.88 476.8
85.03 480.34
47.38 440.63
48.08 459.48
79.65 490.78
83.39 483.56
82.18 429.38
51.71 440.27
77.33 445.34
72.81 447.43
84.26 439.91
73.23 459.27
79.73 478.89
62.32 466.7
78.58 463.5
79.88 436.21
65.87 443.94
80.28 439.63
71.33 460.95
70.33 448.69
57.73 444.63
99.46 473.51
68.61 462.56
95.91 451.76
80.42 491.81
51.01 429.52
74.08 437.9
80.73 467.54
54.71 449.97
73.75 436.62
88.43 477.68
74.66 447.26
70.04 439.76
74.64 437.49
85.11 455.14
82.97 485.5
55.59 444.1
49.9 432.33
89.99 471.23
91.61 463.89
82.95 445.54
92.62 446.09
59.64 445.12
63.0 443.31
85.38 484.16
85.23 477.76
52.08 430.28
38.05 446.48
71.98 481.03
90.66 466.07
83.14 447.47
65.22 455.93
91.67 479.62
66.04 455.06
78.19 475.06
54.47 438.89
67.26 432.7
72.56 452.6
82.15 451.75
86.32 430.66
88.17 491.9
72.78 439.82
69.58 460.73
69.86 449.7
65.37 439.42
52.37 439.84
79.63 485.86
83.14 458.1
88.25 479.92
55.85 458.29
52.55 489.45
62.74 434.0
90.08 431.24
54.5 439.5
49.88 467.46
48.96 429.27
86.77 452.1
96.66 472.41
70.84 442.14
83.83 441.0
68.22 463.07
82.22 445.71
87.9 483.16
66.83 440.45
85.36 481.83
60.9 467.6
83.51 450.88
52.96 425.5
73.02 451.87
43.11 428.94
61.41 439.86
65.32 433.44
93.68 438.23
42.39 436.95
68.18 470.19
89.18 484.66
64.79 430.81
43.48 433.37
80.4 453.02
72.43 453.5
80.0 463.09
45.65 464.56
63.02 452.12
74.39 470.9
57.77 450.89
76.8 445.04
67.39 444.72
73.96 460.38
72.75 446.8
71.69 465.05
84.98 484.13
87.68 488.27
50.36 447.09
68.11 452.02
66.27 455.55
89.72 480.99
61.07 467.68
RH PE
73.17 463.26
59.08 444.37
92.14 488.56
76.64 446.48
96.62 473.9
58.77 443.67
75.24 467.35
66.43 478.42
41.25 475.98
70.72 477.5
75.04 453.02
64.22 453.99
84.15 440.29
61.83 451.28
87.59 433.99
43.08 462.19
48.84 467.54
77.51 477.2
63.59 459.85
55.28 464.3
66.26 468.27
64.77 495.24
83.31 483.8
47.19 443.61
54.93 436.06
74.62 443.25
72.52 464.16
88.44 475.52
92.28 484.41
41.85 437.89
44.28 445.11
64.58 438.86
63.25 440.98
78.61 436.65
44.51 444.26
89.46 465.86
74.52 444.37
88.86 450.69
75.51 469.02
78.64 448.86
76.65 447.14
80.44 469.18
79.89 482.8
88.28 476.7
84.6 474.99
42.69 444.22
78.41 461.33
61.07 448.06
50.0 474.6
77.29 473.05
43.66 432.06
83.8 467.41
66.47 430.12
93.09 473.62
80.52 471.81
68.99 442.99
57.27 442.77
95.53 491.49
71.72 447.46
57.88 446.11
63.34 442.44
48.07 446.22
91.87 471.49
87.27 463.5
64.4 440.01
43.4 441.03
72.24 452.68
90.22 474.91
74.0 478.77
71.85 434.2
86.62 437.91
97.41 477.61
84.44 431.65
81.55 430.57
75.66 481.09
79.41 445.56
58.91 475.74
90.06 435.12
79.0 446.15
69.47 436.64
51.47 436.69
83.13 468.75
40.33 466.6
81.69 465.48
94.55 441.34
91.81 441.83
63.62 464.7
49.35 437.99
69.61 459.12
38.75 429.69
90.17 459.8
81.24 433.63
48.46 442.84
76.72 485.13
51.16 459.12
76.34 445.31
67.3 480.8
52.38 432.55
76.44 443.86
91.55 449.77
71.9 470.71
80.05 452.17
63.77 478.29
62.26 428.54
89.04 478.27
58.02 439.58
81.82 457.32
91.14 475.51
88.92 439.66
84.83 471.99
91.76 479.81
86.56 434.78
57.21 446.58
54.25 437.76
63.8 459.36
33.71 462.28
67.25 464.33
60.11 444.36
74.55 438.64
67.34 470.49
42.75 455.13
55.2 450.22
83.61 440.43
88.78 482.98
100.12 460.44
64.52 444.97
51.41 433.94
85.78 439.73
75.41 434.48
81.63 442.33
51.92 457.67
70.12 454.66
53.83 432.21
77.23 457.66
65.67 435.21
71.18 448.22
81.96 475.51
79.54 446.53
47.09 441.3
57.69 433.54
78.89 472.52
85.29 474.77
40.13 435.1
77.06 450.74
67.38 442.7
62.44 426.56
77.43 463.71
58.77 447.06
67.72 452.27
42.14 445.78
84.16 438.65
89.79 480.15
67.21 447.19
72.14 443.04
97.49 488.81
87.74 455.75
96.3 455.86
61.25 457.68
88.38 479.11
74.77 432.84
68.18 448.37
77.2 447.06
49.54 443.53
92.22 445.21
33.65 441.7
64.59 450.93
100.09 451.44
68.04 441.29
48.94 458.85
74.47 481.46
81.02 467.19
71.17 461.54
53.85 439.08
70.67 467.22
59.36 468.8
57.17 426.93
70.29 474.65
83.37 468.97
87.36 433.97
100.09 450.53
68.78 444.51
70.98 469.03
75.68 466.56
47.49 457.57
71.99 440.13
66.55 433.24
74.73 452.55
64.78 443.29
75.13 431.76
56.38 454.97
94.35 456.7
86.55 486.03
82.95 472.79
88.42 452.03
85.61 443.41
58.39 441.93
74.28 432.64
87.85 480.25
83.5 466.68
65.24 494.39
75.01 454.72
84.52 448.71
80.52 469.76
75.14 450.71
75.75 444.01
76.72 453.2
85.47 450.87
57.95 441.73
78.32 465.09
52.2 447.28
93.69 491.16
75.74 450.98
67.56 446.3
69.46 436.48
74.58 460.84
53.23 442.56
88.72 467.3
96.16 479.13
68.26 441.15
86.39 445.52
85.34 475.4
72.64 469.3
97.82 463.57
77.22 445.32
80.59 461.03
46.91 466.74
57.76 444.04
53.09 434.01
84.31 465.23
71.58 440.6
92.97 466.74
74.55 433.48
78.96 473.59
64.44 474.81
68.23 454.75
70.81 452.94
61.66 435.83
77.76 482.19
69.49 466.66
96.26 462.59
55.74 447.82
95.61 462.73
84.75 447.98
75.3 462.72
67.5 442.42
80.92 444.69
79.23 466.7
81.1 453.84
32.8 436.92
84.31 486.37
46.15 440.43
53.96 446.82
59.83 484.91
75.3 437.76
42.53 438.91
70.58 464.19
91.69 442.19
63.55 446.86
61.51 457.15
69.55 482.57
98.08 476.03
79.34 428.89
81.28 472.7
78.99 445.6
80.38 464.78
51.16 440.42
72.17 428.41
75.39 438.5
68.91 438.28
96.38 476.29
70.54 448.46
45.8 438.99
57.95 471.8
81.89 471.81
69.32 449.82
59.14 442.14
81.54 441.46
85.81 477.62
65.41 446.76
81.15 472.52
95.87 471.58
90.24 440.85
75.13 431.37
88.22 437.33
81.48 469.22
89.84 471.11
43.57 439.17
63.16 445.33
57.14 473.71
77.76 452.66
90.56 440.99
60.98 467.42
70.31 444.14
74.05 457.17
75.42 467.87
82.25 442.04
67.95 471.36
100.09 460.7
47.28 431.33
72.41 432.6
77.67 447.61
63.7 443.87
79.77 446.87
93.84 465.74
84.95 447.86
70.16 447.65
84.24 437.87
73.32 483.51
86.17 479.65
65.43 455.16
94.59 431.91
86.8 470.68
58.18 429.28
89.66 450.81
87.39 437.73
36.35 460.21
79.62 442.86
50.52 482.99
51.96 440.0
74.73 478.48
78.33 455.28
85.19 436.94
83.13 461.06
53.49 438.28
88.86 472.61
60.89 426.85
61.14 470.18
68.29 455.38
57.62 428.32
83.63 480.35
78.1 455.56
66.34 447.66
79.02 443.06
68.96 452.43
71.13 477.81
87.01 431.66
74.3 431.8
77.62 446.67
59.56 445.26
41.66 425.72
73.27 430.58
77.16 439.86
67.02 441.11
52.8 434.72
39.04 434.01
65.47 475.64
74.32 460.44
69.22 436.4
93.88 461.03
69.83 479.08
84.11 435.76
78.65 460.14
69.31 442.2
70.3 447.69
68.23 431.15
71.76 445.0
85.88 431.59
71.09 467.22
52.67 445.33
89.68 470.57
73.66 473.77
58.94 447.67
87.05 474.29
67.0 437.14
43.18 432.56
80.62 459.14
59.72 446.19
72.1 428.1
69.15 468.46
55.66 435.02
61.19 445.52
74.62 462.69
73.35 455.75
68.85 463.74
39.89 439.79
53.16 443.26
52.97 432.04
79.87 465.86
84.09 465.6
100.15 469.43
79.77 440.75
88.99 481.32
76.14 479.87
69.13 458.59
93.03 438.62
77.92 445.59
74.89 481.87
88.7 475.01
62.94 436.54
89.62 456.63
81.04 451.69
94.53 463.04
64.02 446.1
70.57 438.67
70.32 466.88
84.86 444.6
81.41 440.26
89.45 483.92
82.71 475.19
93.93 479.24
70.6 434.92
87.68 454.16
87.58 447.58
74.4 467.9
67.35 426.29
63.61 447.02
76.89 455.85
78.08 476.46
69.17 437.48
53.31 452.77
93.32 491.54
42.47 438.41
82.58 476.1
94.59 464.58
86.31 467.74
72.57 442.12
80.76 453.34
71.93 425.29
47.54 449.63
95.72 462.88
77.03 464.67
80.49 489.96
77.67 482.38
78.72 437.95
58.77 429.2
74.8 453.34
51.34 442.47
90.41 462.6
91.1 478.79
62.57 456.11
84.27 450.33
42.93 434.83
40.96 433.43
76.53 456.02
69.74 485.23
74.99 473.57
70.45 469.94
91.49 452.07
88.97 475.32
89.13 480.69
46.52 444.01
60.55 465.17
88.71 480.61
89.15 476.04
83.02 441.76
75.19 428.24
87.35 444.77
85.66 463.1
91.66 470.5
63.47 431.0
72.25 430.68
70.58 436.42
60.1 452.33
89.29 440.16
67.43 435.75
67.58 449.74
70.8 430.73
63.62 432.75
66.68 446.79
90.76 486.35
75.34 453.18
59.77 458.31
80.79 480.26
74.1 448.65
41.34 458.41
58.78 435.39
97.78 450.21
74.85 459.59
69.84 445.84
75.36 441.08
85.8 467.33
90.11 444.19
61.63 432.96
44.76 438.09
89.7 467.9
72.51 475.72
74.98 477.51
79.59 435.13
78.42 477.9
61.23 457.26
47.56 467.53
93.06 465.15
89.65 474.28
50.5 444.49
44.84 452.84
85.32 435.38
82.94 433.57
67.26 435.27
79.05 468.49
62.03 433.07
94.36 430.63
60.02 440.74
95.46 474.49
84.92 449.74
62.8 436.73
90.81 434.58
80.9 473.93
55.84 435.99
75.3 466.83
37.34 427.22
79.5 444.07
87.29 469.57
81.5 459.89
76.42 479.59
75.75 440.92
84.95 480.87
62.37 441.9
49.25 430.2
74.16 465.16
90.55 471.32
94.28 485.43
63.31 495.35
78.9 449.12
90.97 480.53
87.34 457.07
80.8 443.67
90.95 477.52
69.97 472.95
89.45 472.54
76.08 469.17
83.35 435.21
92.16 477.78
58.42 475.89
85.06 483.9
88.91 476.2
83.33 462.16
88.49 471.05
96.88 484.71
73.86 446.34
65.17 469.02
69.41 432.12
81.23 467.28
54.07 429.66
89.17 469.49
78.85 485.87
84.44 481.95
83.02 479.03
90.66 434.5
75.29 464.9
82.6 452.71
45.4 429.74
66.33 457.09
45.33 446.77
67.12 460.76
84.14 471.95
80.81 453.29
49.13 441.61
87.29 464.73
52.95 464.68
68.92 430.59
85.21 438.01
88.56 479.08
55.09 436.39
48.64 447.07
87.85 479.91
87.42 489.05
62.75 463.17
94.86 471.26
63.54 480.49
69.46 473.78
74.66 455.5
80.57 446.27
84.7 482.2
72.6 452.48
52.63 464.48
82.01 438.1
75.22 445.6
51.05 442.43
80.1 436.67
81.58 466.56
65.94 457.29
86.74 487.03
62.57 464.93
57.37 466.0
88.91 469.52
72.26 428.88
74.98 474.3
71.19 461.06
62.82 465.57
55.31 467.67
71.57 466.99
59.16 463.72
40.8 443.78
67.63 445.23
97.2 464.43
91.16 484.36
64.81 442.16
85.61 464.11
93.42 462.48
77.36 477.49
67.03 437.04
89.45 457.09
54.84 450.6
53.48 465.78
54.47 427.1
43.36 459.81
48.92 447.36
81.22 488.92
60.35 433.36
75.98 483.35
74.24 469.53
85.21 476.96
68.46 440.75
78.31 462.55
89.25 448.04
68.57 455.24
67.38 494.75
53.6 444.58
91.69 484.82
78.21 442.9
94.19 485.46
37.19 457.81
83.53 481.92
79.45 443.23
99.9 474.29
50.39 430.46
74.33 455.71
83.66 438.34
89.48 485.83
64.59 452.82
75.68 435.04
64.18 451.21
70.09 465.81
70.58 458.42
99.28 470.22
81.89 449.24
87.99 471.43
88.21 473.26
91.29 452.82
52.72 432.69
67.5 444.13
92.05 467.21
63.23 445.98
90.88 436.91
74.91 455.01
85.39 437.11
96.98 477.06
56.28 441.71
65.62 495.76
55.32 445.63
88.88 464.72
39.49 438.03
54.59 434.78
57.19 444.67
45.06 452.24
40.62 450.92
90.21 436.53
90.91 435.53
74.96 440.01
54.21 443.1
63.62 427.49
50.04 436.25
51.23 440.74
82.71 443.54
92.04 459.42
90.67 439.66
91.14 464.15
70.43 459.1
66.63 455.68
86.95 469.08
96.69 478.02
70.88 456.8
47.14 441.13
63.36 463.88
60.58 430.45
54.3 449.18
65.09 447.89
48.16 431.59
81.51 447.5
68.57 475.58
73.16 453.24
80.88 446.4
85.4 476.81
75.77 474.1
75.76 450.71
70.21 433.62
55.53 465.14
80.48 445.18
72.41 474.12
83.25 483.91
82.12 486.68
94.75 464.98
95.79 481.4
86.02 479.2
78.29 463.86
82.23 472.3
52.86 446.51
60.66 437.71
62.77 458.94
65.54 437.91
95.4 490.76
51.78 439.66
63.62 463.27
83.09 473.99
61.81 433.38
68.24 459.01
72.41 471.44
79.64 471.91
66.95 465.15
91.98 446.66
64.96 438.15
88.93 447.14
85.62 472.32
84.0 441.68
89.41 440.04
67.4 444.82
76.75 457.26
89.06 428.83
64.02 449.07
64.12 435.21
81.22 471.03
100.13 465.56
58.07 442.83
63.42 460.3
83.32 474.25
74.28 477.97
71.91 472.16
85.8 456.08
55.58 452.41
69.7 463.71
63.79 433.72
86.59 456.4
48.28 448.43
80.42 481.6
98.58 457.07
72.83 451.0
56.07 440.28
67.13 437.47
84.49 443.57
68.37 426.6
86.07 470.87
83.82 478.37
74.86 453.92
53.52 470.22
80.61 434.54
43.56 442.89
89.35 479.03
97.28 476.06
80.49 473.88
88.9 451.75
49.7 439.2
68.64 439.7
98.58 463.6
82.12 447.47
78.32 447.92
86.04 471.08
91.36 437.55
81.02 448.27
76.05 431.69
71.81 449.09
82.13 448.79
74.27 460.21
71.32 479.28
74.59 483.11
84.44 450.75
43.39 437.97
87.2 459.76
77.11 457.75
82.81 469.33
85.67 433.28
95.58 444.64
74.46 463.1
90.02 460.91
81.93 479.35
86.29 449.23
85.43 474.51
71.66 435.02
71.33 435.45
67.72 452.38
84.23 480.41
74.44 478.96
71.48 468.87
56.3 434.01
68.13 466.36
68.35 435.28
85.23 486.46
79.78 468.19
98.98 468.37
72.87 474.19
90.93 440.32
72.94 485.32
72.3 464.27
77.74 479.25
78.29 430.4
69.1 447.49
55.79 438.23
75.09 492.09
88.98 475.36
64.26 452.56
25.89 427.84
59.18 433.95
67.48 435.27
89.85 454.62
50.62 472.17
83.97 452.42
96.51 472.17
80.09 481.83
84.02 458.78
61.97 447.5
88.51 463.4
81.83 473.57
90.63 433.72
73.37 431.85
77.5 433.47
57.46 432.84
51.91 436.6
79.14 490.23
69.24 477.16
41.85 441.06
95.1 440.86
74.53 477.94
64.85 474.47
57.07 470.67
62.9 447.31
72.21 466.8
65.99 430.91
73.67 434.75
88.59 469.52
61.19 438.9
49.37 429.56
48.65 432.92
56.18 442.87
71.56 466.59
87.46 479.61
70.02 471.08
61.2 433.37
60.54 443.92
71.82 443.5
44.8 439.89
67.32 434.66
78.77 487.57
96.02 464.64
90.56 470.92
83.19 444.39
68.45 442.48
99.19 449.61
88.11 435.02
79.29 458.67
87.76 461.74
82.56 438.31
79.24 462.38
67.24 460.56
58.98 439.22
84.22 444.64
89.12 430.34
50.07 430.46
98.86 456.79
95.79 468.82
70.06 448.51
41.71 470.77
86.55 465.74
71.97 430.21
96.4 449.23
91.73 461.89
91.62 445.72
59.14 466.13
92.56 448.71
83.71 469.25
55.43 450.56
74.91 464.46
89.41 471.13
69.81 461.52
86.01 451.09
86.05 431.51
80.98 469.8
63.62 442.28
64.16 458.67
75.63 462.4
80.21 453.54
59.7 444.38
47.6 440.52
63.78 433.62
89.37 481.96
70.55 452.75
84.42 481.28
80.62 439.03
52.56 435.75
83.26 436.03
70.64 445.6
89.95 462.65
51.53 438.66
84.83 447.32
59.68 484.55
97.88 476.8
85.03 480.34
47.38 440.63
48.08 459.48
79.65 490.78
83.39 483.56
82.18 429.38
51.71 440.27
77.33 445.34
72.81 447.43
84.26 439.91
73.23 459.27
79.73 478.89
62.32 466.7
78.58 463.5
79.88 436.21
65.87 443.94
80.28 439.63
71.33 460.95
70.33 448.69
57.73 444.63
99.46 473.51
68.61 462.56
95.91 451.76
80.42 491.81
51.01 429.52
74.08 437.9
80.73 467.54
54.71 449.97
73.75 436.62
88.43 477.68
74.66 447.26
70.04 439.76
74.64 437.49
85.11 455.14
82.97 485.5
55.59 444.1
49.9 432.33
89.99 471.23
91.61 463.89
82.95 445.54
92.62 446.09
59.64 445.12
63.0 443.31
85.38 484.16
85.23 477.76
52.08 430.28
38.05 446.48
71.98 481.03
90.66 466.07
83.14 447.47
65.22 455.93
91.67 479.62
66.04 455.06
78.19 475.06
54.47 438.89
67.26 432.7
72.56 452.6
82.15 451.75
86.32 430.66
88.17 491.9
72.78 439.82
69.58 460.73
69.86 449.7
65.37 439.42
52.37 439.84
79.63 485.86
83.14 458.1
88.25 479.92
55.85 458.29
52.55 489.45
62.74 434.0
90.08 431.24
54.5 439.5
49.88 467.46
48.96 429.27
86.77 452.1
96.66 472.41
70.84 442.14
83.83 441.0
68.22 463.07
82.22 445.71
87.9 483.16
66.83 440.45
85.36 481.83
60.9 467.6
83.51 450.88
52.96 425.5
73.02 451.87
43.11 428.94
61.41 439.86
65.32 433.44
93.68 438.23
42.39 436.95
68.18 470.19
89.18 484.66
64.79 430.81
43.48 433.37
80.4 453.02
72.43 453.5
80.0 463.09
45.65 464.56
63.02 452.12
74.39 470.9
57.77 450.89
76.8 445.04
67.39 444.72
73.96 460.38
72.75 446.8
71.69 465.05
84.98 484.13
87.68 488.27
50.36 447.09
68.11 452.02
66.27 455.55
89.72 480.99
61.07 467.68
AT V AP RH PE
14.96 41.76 1024.07 73.17 463.26
25.18 62.96 1020.04 59.08 444.37
5.11 39.4 1012.16 92.14 488.56
20.86 57.32 1010.24 76.64 446.48
10.82 37.5 1009.23 96.62 473.9
26.27 59.44 1012.23 58.77 443.67
15.89 43.96 1014.02 75.24 467.35
9.48 44.71 1019.12 66.43 478.42
14.64 45.0 1021.78 41.25 475.98
11.74 43.56 1015.14 70.72 477.5
17.99 43.72 1008.64 75.04 453.02
20.14 46.93 1014.66 64.22 453.99
24.34 73.5 1011.31 84.15 440.29
25.71 58.59 1012.77 61.83 451.28
26.19 69.34 1009.48 87.59 433.99
21.42 43.79 1015.76 43.08 462.19
18.21 45.0 1022.86 48.84 467.54
11.04 41.74 1022.6 77.51 477.2
14.45 52.75 1023.97 63.59 459.85
13.97 38.47 1015.15 55.28 464.3
17.76 42.42 1009.09 66.26 468.27
5.41 40.07 1019.16 64.77 495.24
7.76 42.28 1008.52 83.31 483.8
27.23 63.9 1014.3 47.19 443.61
27.36 48.6 1003.18 54.93 436.06
27.47 70.72 1009.97 74.62 443.25
14.6 39.31 1011.11 72.52 464.16
7.91 39.96 1023.57 88.44 475.52
5.81 35.79 1012.14 92.28 484.41
30.53 65.18 1012.69 41.85 437.89
23.87 63.94 1019.02 44.28 445.11
26.09 58.41 1013.64 64.58 438.86
29.27 66.85 1011.11 63.25 440.98
27.38 74.16 1010.08 78.61 436.65
24.81 63.94 1018.76 44.51 444.26
12.75 44.03 1007.29 89.46 465.86
24.66 63.73 1011.4 74.52 444.37
16.38 47.45 1010.08 88.86 450.69
13.91 39.35 1014.69 75.51 469.02
23.18 51.3 1012.04 78.64 448.86
22.47 47.45 1007.62 76.65 447.14
13.39 44.85 1017.24 80.44 469.18
9.28 41.54 1018.33 79.89 482.8
11.82 42.86 1014.12 88.28 476.7
10.27 40.64 1020.63 84.6 474.99
22.92 63.94 1019.28 42.69 444.22
16.0 37.87 1020.24 78.41 461.33
21.22 43.43 1010.96 61.07 448.06
13.46 44.71 1014.51 50.0 474.6
9.39 40.11 1029.14 77.29 473.05
31.07 73.5 1010.58 43.66 432.06
12.82 38.62 1018.71 83.8 467.41
32.57 78.92 1011.6 66.47 430.12
8.11 42.18 1014.82 93.09 473.62
13.92 39.39 1012.94 80.52 471.81
23.04 59.43 1010.23 68.99 442.99
27.31 64.44 1014.65 57.27 442.77
5.91 39.33 1010.18 95.53 491.49
25.26 61.08 1013.68 71.72 447.46
27.97 58.84 1002.25 57.88 446.11
26.08 52.3 1007.03 63.34 442.44
29.01 65.71 1013.61 48.07 446.22
12.18 40.1 1016.67 91.87 471.49
13.76 45.87 1008.89 87.27 463.5
25.5 58.79 1016.02 64.4 440.01
28.26 65.34 1014.56 43.4 441.03
21.39 62.96 1019.49 72.24 452.68
7.26 40.69 1020.43 90.22 474.91
10.54 34.03 1018.71 74.0 478.77
27.71 74.34 998.14 71.85 434.2
23.11 68.3 1017.83 86.62 437.91
7.51 41.01 1024.61 97.41 477.61
26.46 74.67 1016.65 84.44 431.65
29.34 74.34 998.58 81.55 430.57
10.32 42.28 1008.82 75.66 481.09
22.74 61.02 1009.56 79.41 445.56
13.48 39.85 1012.71 58.91 475.74
25.52 69.75 1010.36 90.06 435.12
21.58 67.25 1017.39 79.0 446.15
27.66 76.86 1001.31 69.47 436.64
26.96 69.45 1013.89 51.47 436.69
12.29 42.18 1016.53 83.13 468.75
15.86 43.02 1012.18 40.33 466.6
13.87 45.08 1024.42 81.69 465.48
24.09 73.68 1014.93 94.55 441.34
20.45 69.45 1012.53 91.81 441.83
15.07 39.3 1019.0 63.62 464.7
32.72 69.75 1009.6 49.35 437.99
18.23 58.96 1015.55 69.61 459.12
35.56 68.94 1006.56 38.75 429.69
18.36 51.43 1010.57 90.17 459.8
26.35 64.05 1009.81 81.24 433.63
25.92 60.95 1014.62 48.46 442.84
8.01 41.66 1014.49 76.72 485.13
19.63 52.72 1025.09 51.16 459.12
20.02 67.32 1012.05 76.34 445.31
10.08 40.72 1022.7 67.3 480.8
27.23 66.48 1005.23 52.38 432.55
23.37 63.77 1013.42 76.44 443.86
18.74 59.21 1018.3 91.55 449.77
14.81 43.69 1017.19 71.9 470.71
23.1 51.3 1011.93 80.05 452.17
10.72 41.38 1021.6 63.77 478.29
29.46 71.94 1006.96 62.26 428.54
8.1 40.64 1020.66 89.04 478.27
27.29 62.66 1007.63 58.02 439.58
17.1 49.69 1005.53 81.82 457.32
11.49 44.2 1018.79 91.14 475.51
23.69 65.59 1010.85 88.92 439.66
13.51 40.89 1011.03 84.83 471.99
9.64 39.35 1015.1 91.76 479.81
25.65 78.92 1010.83 86.56 434.78
21.59 61.87 1011.18 57.21 446.58
27.98 58.33 1013.92 54.25 437.76
18.8 39.72 1001.24 63.8 459.36
18.28 44.71 1016.99 33.71 462.28
13.55 43.48 1016.08 67.25 464.33
22.99 46.21 1010.71 60.11 444.36
23.94 59.39 1014.32 74.55 438.64
13.74 34.03 1018.69 67.34 470.49
21.3 41.1 1001.86 42.75 455.13
27.54 66.93 1017.06 55.2 450.22
24.81 63.73 1009.34 83.61 440.43
4.97 42.85 1014.02 88.78 482.98
15.22 50.88 1014.19 100.12 460.44
23.88 54.2 1012.81 64.52 444.97
33.01 68.67 1005.2 51.41 433.94
25.98 73.18 1012.28 85.78 439.73
28.18 73.88 1005.89 75.41 434.48
21.67 60.84 1017.93 81.63 442.33
17.67 45.09 1014.26 51.92 457.67
21.37 57.76 1018.8 70.12 454.66
28.69 67.25 1017.71 53.83 432.21
16.61 43.77 1012.25 77.23 457.66
27.91 63.76 1010.27 65.67 435.21
20.97 47.43 1007.64 71.18 448.22
10.8 41.66 1013.79 81.96 475.51
20.61 62.91 1013.24 79.54 446.53
25.45 57.32 1011.7 47.09 441.3
30.16 69.34 1007.67 57.69 433.54
4.99 39.04 1020.45 78.89 472.52
10.51 44.78 1012.59 85.29 474.77
33.79 69.05 1001.62 40.13 435.1
21.34 59.8 1016.92 77.06 450.74
23.4 65.06 1014.32 67.38 442.7
32.21 68.14 1003.34 62.44 426.56
14.26 42.32 1016.0 77.43 463.71
27.71 66.93 1016.85 58.77 447.06
21.95 57.76 1018.02 67.72 452.27
25.76 63.94 1018.49 42.14 445.78
23.68 68.3 1017.93 84.16 438.65
8.28 40.77 1011.55 89.79 480.15
23.44 62.52 1016.46 67.21 447.19
25.32 48.41 1008.47 72.14 443.04
3.94 39.9 1008.06 97.49 488.81
17.3 57.76 1016.26 87.74 455.75
18.2 49.39 1018.83 96.3 455.86
21.43 46.97 1013.94 61.25 457.68
11.16 40.05 1014.95 88.38 479.11
30.38 74.16 1007.44 74.77 432.84
23.36 62.52 1016.18 68.18 448.37
21.69 47.45 1007.56 77.2 447.06
23.62 49.21 1014.1 49.54 443.53
21.87 61.45 1011.13 92.22 445.21
29.25 66.51 1015.53 33.65 441.7
20.03 66.86 1013.05 64.59 450.93
18.14 49.78 1002.95 100.09 451.44
24.23 56.89 1012.32 68.04 441.29
18.11 44.85 1014.48 48.94 458.85
6.57 43.65 1018.24 74.47 481.46
12.56 43.41 1016.93 81.02 467.19
13.4 41.58 1020.5 71.17 461.54
27.1 52.84 1006.28 53.85 439.08
14.28 42.74 1028.79 70.67 467.22
16.29 44.34 1019.49 59.36 468.8
31.24 71.98 1004.66 57.17 426.93
10.57 37.73 1024.36 70.29 474.65
13.8 44.21 1022.93 83.37 468.97
25.3 71.58 1010.18 87.36 433.97
18.06 50.16 1009.52 100.09 450.53
25.42 59.04 1011.98 68.78 444.51
15.07 40.69 1015.29 70.98 469.03
11.75 71.14 1019.36 75.68 466.56
20.23 52.05 1012.15 47.49 457.57
27.31 59.54 1006.24 71.99 440.13
28.57 69.84 1003.57 66.55 433.24
17.9 43.72 1008.64 74.73 452.55
23.83 71.37 1002.04 64.78 443.29
27.92 74.99 1005.47 75.13 431.76
17.34 44.78 1007.81 56.38 454.97
17.94 63.07 1012.42 94.35 456.7
6.4 39.9 1007.75 86.55 486.03
11.78 39.96 1011.37 82.95 472.79
20.28 57.25 1010.12 88.42 452.03
21.04 54.2 1012.26 85.61 443.41
25.11 67.32 1014.49 58.39 441.93
30.28 70.98 1007.51 74.28 432.64
8.14 36.24 1013.15 87.85 480.25
16.86 39.63 1004.47 83.5 466.68
6.25 40.07 1020.19 65.24 494.39
22.35 54.42 1012.46 75.01 454.72
17.98 56.85 1012.28 84.52 448.71
21.19 42.48 1013.43 80.52 469.76
20.94 44.89 1009.64 75.14 450.71
24.23 58.79 1009.8 75.75 444.01
19.18 58.2 1017.46 76.72 453.2
20.88 57.85 1012.39 85.47 450.87
23.67 63.86 1019.67 57.95 441.73
14.12 39.52 1018.41 78.32 465.09
25.23 64.63 1020.59 52.2 447.28
6.54 39.33 1011.54 93.69 491.16
20.08 62.52 1017.99 75.74 450.98
24.67 63.56 1013.75 67.56 446.3
27.82 79.74 1008.37 69.46 436.48
15.55 42.03 1017.41 74.58 460.84
24.26 69.51 1013.43 53.23 442.56
13.45 41.49 1020.19 88.72 467.3
11.06 40.64 1021.47 96.16 479.13
24.91 52.3 1008.72 68.26 441.15
22.39 59.04 1011.78 86.39 445.52
11.95 40.69 1015.62 85.34 475.4
14.85 40.69 1014.91 72.64 469.3
10.11 41.62 1017.17 97.82 463.57
23.67 68.67 1006.71 77.22 445.32
16.14 44.21 1020.36 80.59 461.03
15.11 43.13 1014.99 46.91 466.74
24.14 59.87 1018.47 57.76 444.04
30.08 67.25 1017.6 53.09 434.01
14.77 44.9 1020.5 84.31 465.23
27.6 69.34 1009.63 71.58 440.6
13.89 44.84 1023.66 92.97 466.74
26.85 75.6 1017.43 74.55 433.48
12.41 40.96 1023.36 78.96 473.59
13.08 41.74 1020.75 64.44 474.81
18.93 44.06 1017.58 68.23 454.75
20.5 49.69 1009.6 70.81 452.94
30.72 69.13 1009.94 61.66 435.83
7.55 39.22 1014.53 77.76 482.19
13.49 44.47 1030.46 69.49 466.66
15.62 40.12 1013.03 96.26 462.59
24.8 64.63 1020.69 55.74 447.82
10.03 41.62 1014.55 95.61 462.73
22.43 63.21 1012.06 84.75 447.98
14.95 39.31 1009.15 75.3 462.72
24.78 58.46 1016.82 67.5 442.42
23.2 48.41 1008.64 80.92 444.69
14.01 39.0 1016.73 79.23 466.7
19.4 64.63 1020.38 81.1 453.84
30.15 67.32 1013.83 32.8 436.92
6.91 36.08 1021.82 84.31 486.37
29.04 60.07 1015.42 46.15 440.43
26.02 63.07 1010.94 53.96 446.82
5.89 39.48 1005.11 59.83 484.91
26.52 71.64 1008.27 75.3 437.76
28.53 68.08 1013.27 42.53 438.91
16.59 39.54 1007.97 70.58 464.19
22.95 67.79 1009.89 91.69 442.19
23.96 47.43 1008.38 63.55 446.86
17.48 44.2 1018.89 61.51 457.15
6.69 43.65 1020.14 69.55 482.57
10.25 41.26 1007.44 98.08 476.03
28.87 72.58 1008.69 79.34 428.89
12.04 40.23 1018.07 81.28 472.7
22.58 52.3 1009.04 78.99 445.6
15.12 52.05 1014.63 80.38 464.78
25.48 58.95 1017.02 51.16 440.42
27.87 70.79 1003.96 72.17 428.41
23.72 70.47 1010.65 75.39 438.5
25.0 59.43 1007.84 68.91 438.28
8.42 40.64 1022.35 96.38 476.29
22.46 58.49 1011.5 70.54 448.46
29.92 57.19 1008.62 45.8 438.99
11.68 39.22 1017.9 57.95 471.8
14.04 42.44 1012.74 81.89 471.81
19.86 59.14 1016.12 69.32 449.82
25.99 68.08 1013.13 59.14 442.14
23.42 58.79 1009.74 81.54 441.46
10.6 40.22 1011.37 85.81 477.62
20.97 61.87 1011.45 65.41 446.76
14.14 39.82 1012.46 81.15 472.52
8.56 40.71 1021.27 95.87 471.58
24.86 72.39 1001.15 90.24 440.85
29.0 77.54 1011.33 75.13 431.37
27.59 71.97 1008.64 88.22 437.33
10.45 40.71 1015.68 81.48 469.22
8.51 40.78 1023.51 89.84 471.11
29.82 66.51 1010.98 43.57 439.17
22.56 62.26 1012.11 63.16 445.33
11.38 39.22 1018.62 57.14 473.71
20.25 57.76 1016.28 77.76 452.66
22.42 59.43 1007.12 90.56 440.99
14.85 38.91 1014.48 60.98 467.42
25.62 58.82 1010.02 70.31 444.14
19.85 56.53 1020.57 74.05 457.17
13.67 54.3 1015.92 75.42 467.87
24.39 70.72 1009.78 82.25 442.04
16.07 44.58 1019.52 67.95 471.36
11.6 39.1 1009.81 100.09 460.7
31.38 70.83 1010.35 47.28 431.33
29.91 76.86 998.59 72.41 432.6
19.67 59.39 1014.07 77.67 447.61
27.18 64.79 1016.27 63.7 443.87
21.39 52.3 1009.2 79.77 446.87
10.45 41.01 1020.57 93.84 465.74
19.46 56.89 1014.02 84.95 447.86
23.55 62.96 1020.16 70.16 447.65
23.35 63.47 1011.78 84.24 437.87
9.26 41.66 1016.87 73.32 483.51
10.3 41.46 1018.21 86.17 479.65
20.94 58.16 1016.88 65.43 455.16
23.13 71.25 1002.49 94.59 431.91
12.77 41.5 1014.13 86.8 470.68
28.29 69.13 1009.29 58.18 429.28
19.13 59.21 1018.32 89.66 450.81
24.44 73.5 1011.49 87.39 437.73
20.32 44.6 1015.16 36.35 460.21
20.54 69.05 1001.6 79.62 442.86
12.16 45.0 1021.51 50.52 482.99
28.09 65.27 1013.27 51.96 440.0
9.25 41.82 1033.25 74.73 478.48
21.75 49.82 1015.01 78.33 455.28
23.7 66.56 1002.07 85.19 436.94
16.22 37.87 1022.36 83.13 461.06
24.75 69.45 1013.97 53.49 438.28
10.48 39.58 1011.81 88.86 472.61
29.53 70.79 1003.7 60.89 426.85
12.59 39.72 1017.76 61.14 470.18
23.5 54.42 1012.31 68.29 455.38
29.01 66.56 1006.44 57.62 428.32
9.75 42.49 1010.57 83.63 480.35
19.55 56.53 1020.2 78.1 455.56
21.05 58.33 1013.14 66.34 447.66
24.72 68.67 1006.74 79.02 443.06
21.19 58.86 1014.19 68.96 452.43
10.77 41.54 1019.94 71.13 477.81
28.68 73.77 1004.72 87.01 431.66
29.87 73.91 1004.53 74.3 431.8
22.99 68.67 1006.65 77.62 446.67
24.66 60.29 1018.0 59.56 445.26
32.63 69.89 1013.85 41.66 425.72
31.38 72.29 1008.73 73.27 430.58
23.87 60.27 1018.94 77.16 439.86
25.6 59.15 1013.31 67.02 441.11
27.62 71.14 1011.6 52.8 434.72
30.1 67.45 1014.23 39.04 434.01
12.19 41.17 1019.43 65.47 475.64
13.11 41.58 1020.43 74.32 460.44
28.29 68.67 1005.46 69.22 436.4
13.45 40.73 1018.7 93.88 461.03
10.98 41.54 1019.94 69.83 479.08
26.48 69.14 1009.31 84.11 435.76
13.07 45.51 1015.22 78.65 460.14
25.56 75.6 1017.37 69.31 442.2
22.68 50.78 1008.83 70.3 447.69
28.86 73.67 1006.65 68.23 431.15
22.7 63.56 1014.32 71.76 445.0
27.89 73.21 1001.32 85.88 431.59
13.78 44.47 1027.94 71.09 467.22
28.14 51.43 1012.16 52.67 445.33
11.8 45.09 1013.21 89.68 470.57
10.71 39.61 1018.72 73.66 473.77
24.54 60.29 1017.42 58.94 447.67
11.54 40.05 1014.78 87.05 474.29
29.47 71.32 1008.07 67.0 437.14
29.24 69.05 1003.12 43.18 432.56
14.51 41.79 1009.72 80.62 459.14
22.91 60.07 1016.03 59.72 446.19
27.02 71.77 1006.38 72.1 428.1
13.49 44.47 1030.18 69.15 468.46
30.24 66.75 1017.95 55.66 435.02
23.19 48.6 1002.38 61.19 445.52
17.73 40.55 1003.36 74.62 462.69
18.62 61.27 1019.26 73.35 455.75
12.85 40.0 1015.89 68.85 463.74
32.33 69.68 1011.95 39.89 439.79
25.09 58.95 1016.99 53.16 443.26
29.45 69.13 1009.3 52.97 432.04
16.91 43.96 1013.32 79.87 465.86
14.09 45.87 1009.05 84.09 465.6
10.73 25.36 1009.35 100.15 469.43
23.2 49.3 1003.4 79.77 440.75
8.21 38.91 1015.82 88.99 481.32
9.3 40.56 1022.64 76.14 479.87
16.97 39.16 1005.7 69.13 458.59
23.69 71.97 1009.62 93.03 438.62
25.13 59.44 1012.38 77.92 445.59
9.86 43.56 1015.13 74.89 481.87
11.33 41.5 1013.58 88.7 475.01
26.95 48.41 1008.53 62.94 436.54
15.0 40.66 1016.28 89.62 456.63
20.76 62.52 1015.63 81.04 451.69
14.29 39.59 1010.93 94.53 463.04
19.74 67.71 1007.68 64.02 446.1
26.68 59.92 1009.94 70.57 438.67
14.24 41.4 1019.7 70.32 466.88
21.98 48.41 1008.42 84.86 444.6
22.75 59.39 1015.4 81.41 440.26
8.34 40.96 1023.28 89.45 483.92
11.8 41.2 1017.18 82.71 475.19
8.81 44.68 1023.06 93.93 479.24
30.05 73.68 1014.95 70.6 434.92
16.01 65.46 1014.0 87.68 454.16
21.75 58.79 1012.42 87.58 447.58
13.94 41.26 1021.67 74.4 467.9
29.25 69.13 1010.27 67.35 426.29
22.33 45.87 1007.8 63.61 447.02
16.43 41.79 1005.47 76.89 455.85
11.5 40.22 1010.31 78.08 476.46
23.53 68.94 1007.53 69.17 437.48
21.86 49.21 1014.61 53.31 452.77
6.17 39.33 1012.57 93.32 491.54
30.19 64.79 1017.22 42.47 438.41
11.67 41.93 1019.81 82.58 476.1
15.34 36.99 1007.87 94.59 464.58
11.5 40.78 1023.91 86.31 467.74
25.53 57.17 1010.0 72.57 442.12
21.27 57.5 1014.53 80.76 453.34
28.37 69.13 1010.44 71.93 425.29
28.39 51.43 1011.74 47.54 449.63
13.78 45.78 1025.27 95.72 462.88
14.6 42.32 1015.71 77.03 464.67
5.1 35.57 1027.17 80.49 489.96
7.0 38.08 1020.27 77.67 482.38
26.3 77.95 1009.45 78.72 437.95
30.56 71.98 1004.74 58.77 429.2
21.09 46.63 1013.03 74.8 453.34
28.21 70.02 1010.58 51.34 442.47
15.84 49.69 1015.14 90.41 462.6
10.03 40.96 1024.57 91.1 478.79
20.37 52.05 1012.34 62.57 456.11
21.19 50.16 1005.81 84.27 450.33
33.73 69.88 1007.21 42.93 434.83
29.87 73.68 1015.1 40.96 433.43
19.62 62.96 1020.76 76.53 456.02
9.93 40.67 1018.08 69.74 485.23
9.43 37.14 1013.03 74.99 473.57
14.24 39.58 1011.17 70.45 469.94
12.97 49.83 1008.69 91.49 452.07
7.6 41.04 1021.82 88.97 475.32
8.39 36.24 1013.39 89.13 480.69
25.41 48.06 1013.12 46.52 444.01
18.43 56.03 1020.41 60.55 465.17
10.31 39.82 1012.87 88.71 480.61
11.29 41.5 1013.39 89.15 476.04
22.61 49.3 1003.51 83.02 441.76
29.34 71.98 1005.19 75.19 428.24
18.87 67.71 1004.0 87.35 444.77
13.21 45.87 1008.58 85.66 463.1
11.3 44.6 1018.19 91.66 470.5
29.23 72.99 1007.04 63.47 431.0
27.76 69.4 1004.27 72.25 430.68
29.26 67.17 1006.6 70.58 436.42
25.72 49.82 1016.19 60.1 452.33
23.43 63.94 1010.64 89.29 440.16
25.6 63.76 1010.18 67.43 435.75
22.3 44.57 1008.48 67.58 449.74
27.91 72.24 1010.74 70.8 430.73
30.35 77.17 1009.55 63.62 432.75
21.78 47.43 1007.88 66.68 446.79
7.19 41.39 1018.12 90.76 486.35
20.88 59.8 1015.66 75.34 453.18
24.19 50.23 1015.73 59.77 458.31
9.98 41.54 1019.7 80.79 480.26
23.47 51.3 1011.89 74.1 448.65
26.35 49.5 1012.67 41.34 458.41
29.89 64.69 1006.37 58.78 435.39
19.29 50.16 1010.49 97.78 450.21
17.48 43.14 1018.68 74.85 459.59
25.21 75.6 1017.19 69.84 445.84
23.3 48.78 1018.17 75.36 441.08
15.42 37.85 1009.89 85.8 467.33
21.44 63.09 1016.56 90.11 444.19
29.45 68.27 1007.96 61.63 432.96
29.69 47.93 1002.85 44.76 438.09
15.52 36.99 1006.86 89.7 467.9
11.47 43.67 1012.68 72.51 475.72
9.77 34.69 1027.72 74.98 477.51
22.6 69.84 1006.37 79.59 435.13
8.24 39.61 1017.99 78.42 477.9
17.01 44.2 1019.18 61.23 457.26
19.64 44.6 1015.88 47.56 467.53
10.61 41.58 1021.08 93.06 465.15
12.04 40.1 1014.42 89.65 474.28
29.19 65.71 1013.85 50.5 444.49
21.75 45.09 1014.15 44.84 452.84
23.66 77.54 1008.5 85.32 435.38
27.05 75.33 1003.88 82.94 433.57
29.63 69.71 1009.04 67.26 435.27
18.2 39.63 1005.35 79.05 468.49
32.22 70.8 1009.9 62.03 433.07
26.88 73.56 1004.85 94.36 430.63
29.05 65.74 1013.29 60.02 440.74
8.9 39.96 1026.31 95.46 474.49
18.93 48.6 1005.72 84.92 449.74
27.49 63.76 1010.09 62.8 436.73
23.1 70.79 1006.53 90.81 434.58
11.22 43.13 1017.24 80.9 473.93
31.97 79.74 1007.03 55.84 435.99
13.32 43.22 1009.45 75.3 466.83
31.68 68.24 1005.29 37.34 427.22
23.69 63.77 1013.39 79.5 444.07
13.83 41.49 1020.11 87.29 469.57
18.32 66.51 1015.18 81.5 459.89
11.05 40.71 1024.91 76.42 479.59
22.03 64.69 1007.21 75.75 440.92
10.23 41.46 1020.45 84.95 480.87
23.92 66.54 1009.93 62.37 441.9
29.38 69.68 1011.35 49.25 430.2
17.35 42.86 1014.62 74.16 465.16
9.81 44.45 1021.19 90.55 471.32
4.97 40.64 1020.91 94.28 485.43
5.15 40.07 1012.27 63.31 495.35
21.54 58.49 1010.85 78.9 449.12
7.94 42.02 1006.22 90.97 480.53
18.77 50.66 1014.89 87.34 457.07
21.69 69.94 1010.7 80.8 443.67
10.07 44.68 1023.44 90.95 477.52
13.83 39.64 1012.52 69.97 472.95
10.45 39.69 1003.92 89.45 472.54
11.56 40.71 1015.85 76.08 469.17
23.64 70.04 1011.09 83.35 435.21
10.48 40.22 1004.81 92.16 477.78
13.09 39.85 1012.86 58.42 475.89
10.67 40.23 1017.75 85.06 483.9
12.57 39.16 1016.53 88.91 476.2
14.45 43.34 1015.47 83.33 462.16
14.22 37.85 1011.24 88.49 471.05
6.97 41.26 1010.6 96.88 484.71
20.61 63.86 1015.43 73.86 446.34
14.67 42.28 1007.21 65.17 469.02
29.06 72.86 1004.23 69.41 432.12
14.38 40.1 1015.51 81.23 467.28
32.51 69.98 1013.29 54.07 429.66
11.79 45.09 1013.16 89.17 469.49
8.65 40.56 1023.23 78.85 485.87
9.75 40.81 1026.0 84.44 481.95
9.11 40.02 1031.1 83.02 479.03
23.39 69.13 1010.99 90.66 434.5
14.3 54.3 1015.16 75.29 464.9
17.49 63.94 1020.02 82.6 452.71
31.1 69.51 1010.84 45.4 429.74
19.77 56.65 1020.67 66.33 457.09
28.61 72.29 1011.61 45.33 446.77
13.52 41.48 1014.46 67.12 460.76
13.52 40.83 1008.31 84.14 471.95
17.57 46.21 1014.09 80.81 453.29
28.18 60.07 1016.34 49.13 441.61
14.29 46.18 1017.01 87.29 464.73
18.12 43.69 1016.91 52.95 464.68
31.27 73.91 1003.72 68.92 430.59
26.24 77.95 1014.19 85.21 438.01
7.44 41.04 1021.84 88.56 479.08
29.78 74.78 1009.28 55.09 436.39
23.37 65.46 1016.25 48.64 447.07
10.62 39.58 1011.9 87.85 479.91
5.84 43.02 1013.88 87.42 489.05
14.51 53.82 1016.46 62.75 463.17
11.31 42.02 1001.18 94.86 471.26
11.25 40.67 1011.64 63.54 480.49
9.18 39.42 1025.41 69.46 473.78
19.82 58.16 1016.76 74.66 455.5
24.77 58.41 1013.78 80.57 446.27
9.66 41.06 1021.21 84.7 482.2
21.96 59.8 1016.72 72.6 452.48
18.59 43.14 1011.92 52.63 464.48
24.75 69.89 1015.29 82.01 438.1
24.37 63.47 1012.77 75.22 445.6
29.6 67.79 1010.37 51.05 442.43
25.32 61.25 1011.56 80.1 436.67
16.15 41.85 1016.54 81.58 466.56
15.74 71.14 1019.65 65.94 457.29
5.97 36.25 1029.65 86.74 487.03
15.84 52.72 1026.45 62.57 464.93
14.84 44.63 1019.28 57.37 466.0
12.25 48.79 1017.44 88.91 469.52
27.38 70.04 1011.18 72.26 428.88
8.76 41.48 1018.49 74.98 474.3
15.54 39.31 1009.69 71.19 461.06
18.71 39.39 1014.09 62.82 465.57
13.06 41.78 1012.3 55.31 467.67
12.72 40.71 1016.02 71.57 466.99
19.83 39.39 1013.73 59.16 463.72
27.23 49.16 1004.03 40.8 443.78
24.27 68.28 1005.43 67.63 445.23
11.8 40.66 1017.13 97.2 464.43
6.76 36.25 1028.31 91.16 484.36
25.99 63.07 1012.5 64.81 442.16
16.3 39.63 1004.64 85.61 464.11
16.5 49.39 1018.35 93.42 462.48
10.59 42.49 1009.59 77.36 477.49
26.05 65.59 1012.78 67.03 437.04
19.5 40.79 1003.8 89.45 457.09
22.21 45.01 1012.22 54.84 450.6
17.86 45.0 1023.25 53.48 465.78
29.96 70.04 1010.15 54.47 427.1
19.08 44.63 1020.14 43.36 459.81
23.59 47.43 1006.64 48.92 447.36
3.38 39.64 1011.0 81.22 488.92
26.39 66.49 1012.96 60.35 433.36
8.99 39.04 1021.99 75.98 483.35
10.91 41.04 1026.57 74.24 469.53
13.08 39.82 1012.27 85.21 476.96
23.95 58.46 1017.5 68.46 440.75
15.64 43.71 1024.51 78.31 462.55
18.78 54.2 1012.05 89.25 448.04
20.65 50.59 1016.22 68.57 455.24
4.96 40.07 1011.8 67.38 494.75
23.51 57.32 1012.55 53.6 444.58
5.99 35.79 1011.56 91.69 484.82
23.65 66.05 1019.6 78.21 442.9
5.17 39.33 1009.68 94.19 485.46
26.38 49.5 1012.82 37.19 457.81
6.02 43.65 1013.85 83.53 481.92
23.2 61.02 1009.63 79.45 443.23
8.57 39.69 1000.91 99.9 474.29
30.72 71.58 1009.98 50.39 430.46
21.52 50.66 1013.56 74.33 455.71
22.93 62.26 1011.25 83.66 438.34
5.71 41.31 1003.24 89.48 485.83
18.62 44.06 1017.76 64.59 452.82
27.88 68.94 1007.68 75.68 435.04
22.32 59.8 1016.82 64.18 451.21
14.55 42.74 1028.41 70.09 465.81
17.83 44.92 1025.04 70.58 458.42
9.68 39.96 1026.09 99.28 470.22
19.41 49.39 1020.84 81.89 449.24
13.22 44.92 1023.84 87.99 471.43
12.24 44.92 1023.74 88.21 473.26
19.21 58.49 1011.7 91.29 452.82
29.74 70.32 1008.1 52.72 432.69
23.28 60.84 1017.91 67.5 444.13
8.02 41.92 1029.8 92.05 467.21
22.47 48.6 1002.33 63.23 445.98
27.51 73.77 1002.42 90.88 436.91
17.51 44.9 1009.05 74.91 455.01
23.22 66.56 1002.47 85.39 437.11
11.73 40.64 1020.68 96.98 477.06
21.19 67.71 1006.65 56.28 441.71
5.48 40.07 1019.63 65.62 495.76
24.26 66.44 1011.33 55.32 445.63
12.32 41.62 1012.88 88.88 464.72
31.26 68.94 1005.94 39.49 438.03
32.09 72.86 1003.47 54.59 434.78
24.98 60.32 1015.63 57.19 444.67
27.48 61.41 1012.2 45.06 452.24
21.04 45.09 1014.19 40.62 450.92
27.75 70.4 1006.65 90.21 436.53
22.79 71.77 1005.75 90.91 435.53
24.22 68.51 1013.23 74.96 440.01
27.06 64.45 1008.72 54.21 443.1
29.25 71.94 1007.18 63.62 427.49
26.86 68.08 1012.99 50.04 436.25
29.64 67.79 1009.99 51.23 440.74
19.92 63.31 1015.02 82.71 443.54
18.5 51.43 1010.82 92.04 459.42
23.71 60.23 1009.76 90.67 439.66
14.39 44.84 1023.55 91.14 464.15
19.3 56.65 1020.55 70.43 459.1
24.65 52.36 1014.76 66.63 455.68
13.5 45.51 1015.33 86.95 469.08
9.82 41.26 1007.71 96.69 478.02
18.4 44.06 1017.36 70.88 456.8
28.12 44.89 1009.18 47.14 441.13
17.15 43.69 1017.05 63.36 463.88
30.69 73.67 1006.14 60.58 430.45
28.82 65.71 1014.24 54.3 449.18
21.3 48.92 1010.92 65.09 447.89
30.58 70.04 1010.4 48.16 431.59
21.17 52.3 1009.36 81.51 447.5
9.87 41.82 1033.04 68.57 475.58
22.18 59.8 1016.77 73.16 453.24
24.39 63.21 1012.59 80.88 446.4
10.73 44.92 1025.1 85.4 476.81
9.38 40.46 1019.29 75.77 474.1
20.27 57.76 1016.66 75.76 450.71
24.82 66.48 1006.4 70.21 433.62
16.55 41.66 1011.45 55.53 465.14
20.73 59.87 1019.08 80.48 445.18
9.51 39.22 1015.3 72.41 474.12
8.63 43.79 1016.08 83.25 483.91
6.48 40.27 1010.55 82.12 486.68
14.95 43.52 1022.43 94.75 464.98
5.76 45.87 1010.83 95.79 481.4
10.94 39.04 1021.81 86.02 479.2
15.87 41.16 1005.85 78.29 463.86
12.42 38.25 1012.76 82.23 472.3
29.12 58.84 1001.31 52.86 446.51
29.12 51.43 1005.93 60.66 437.71
19.08 41.1 1001.96 62.77 458.94
31.06 67.17 1007.62 65.54 437.91
5.72 39.33 1009.96 95.4 490.76
26.52 65.06 1013.4 51.78 439.66
13.84 44.9 1007.58 63.62 463.27
13.03 39.52 1016.68 83.09 473.99
25.94 66.49 1012.83 61.81 433.38
16.64 53.82 1015.13 68.24 459.01
14.13 40.75 1016.05 72.41 471.44
13.65 39.28 1012.97 79.64 471.91
14.5 44.47 1028.2 66.95 465.15
19.8 51.19 1008.25 91.98 446.66
25.2 63.76 1009.78 64.96 438.15
20.66 51.19 1008.81 88.93 447.14
12.07 43.71 1025.53 85.62 472.32
25.64 70.72 1010.16 84.0 441.68
23.33 72.99 1009.33 89.41 440.04
29.41 64.05 1009.82 67.4 444.82
16.6 53.16 1014.5 76.75 457.26
27.53 72.58 1009.13 89.06 428.83
20.62 43.43 1009.93 64.02 449.07
26.02 71.94 1009.38 64.12 435.21
12.75 44.2 1017.59 81.22 471.03
12.87 48.04 1012.47 100.13 465.56
25.77 62.96 1019.86 58.07 442.83
14.84 41.48 1017.26 63.42 460.3
7.41 40.71 1023.07 83.32 474.25
8.87 41.82 1033.3 74.28 477.97
9.69 40.46 1019.1 71.91 472.16
16.17 46.97 1014.22 85.8 456.08
26.24 49.82 1014.9 55.58 452.41
13.78 43.22 1011.31 69.7 463.71
26.3 67.07 1006.26 63.79 433.72
17.37 57.76 1016.0 86.59 456.4
23.6 48.98 1015.41 48.28 448.43
8.3 36.08 1020.63 80.42 481.6
18.86 42.18 1001.16 98.58 457.07
22.12 49.39 1019.8 72.83 451.0
28.41 75.6 1018.48 56.07 440.28
29.42 71.32 1002.26 67.13 437.47
18.61 67.71 1004.07 84.49 443.57
27.57 69.84 1004.91 68.37 426.6
12.83 41.5 1013.12 86.07 470.87
9.64 39.85 1012.9 83.82 478.37
19.13 58.66 1013.32 74.86 453.92
15.92 40.56 1020.79 53.52 470.22
24.64 72.24 1011.37 80.61 434.54
27.62 63.9 1013.11 43.56 442.89
8.9 36.24 1013.29 89.35 479.03
9.55 43.99 1020.5 97.28 476.06
10.57 36.71 1022.62 80.49 473.88
19.8 57.25 1010.84 88.9 451.75
25.63 56.85 1012.68 49.7 439.2
24.7 58.46 1015.58 68.64 439.7
15.26 46.18 1013.68 98.58 463.6
20.06 52.84 1004.21 82.12 447.47
19.84 56.89 1013.23 78.32 447.92
11.49 44.63 1020.44 86.04 471.08
23.74 72.43 1007.99 91.36 437.55
22.62 51.3 1012.36 81.02 448.27
29.53 72.39 998.47 76.05 431.69
21.32 48.14 1016.57 71.81 449.09
20.3 58.46 1015.93 82.13 448.79
16.97 44.92 1025.21 74.27 460.21
12.07 41.17 1013.54 71.32 479.28
7.46 41.82 1032.67 74.59 483.11
19.2 54.2 1011.46 84.44 450.75
28.64 66.54 1010.43 43.39 437.97
13.56 41.48 1008.53 87.2 459.76
17.4 44.9 1020.5 77.11 457.75
14.08 40.1 1015.48 82.81 469.33
27.11 69.75 1009.74 85.67 433.28
20.92 70.02 1010.23 95.58 444.64
16.18 44.9 1021.3 74.46 463.1
15.57 44.68 1022.01 90.02 460.91
10.37 39.04 1023.95 81.93 479.35
19.6 59.21 1017.65 86.29 449.23
9.22 40.92 1021.83 85.43 474.51
27.76 72.99 1007.81 71.66 435.02
28.68 70.72 1009.43 71.33 435.45
20.95 48.14 1013.3 67.72 452.38
9.06 39.3 1019.73 84.23 480.41
9.21 39.72 1019.54 74.44 478.96
13.65 42.74 1026.58 71.48 468.87
31.79 76.2 1007.89 56.3 434.01
14.32 44.6 1013.85 68.13 466.36
26.28 75.23 1011.44 68.35 435.28
7.69 43.02 1014.51 85.23 486.46
14.44 40.1 1015.51 79.78 468.19
9.19 41.01 1022.14 98.98 468.37
13.35 41.39 1019.17 72.87 474.19
23.04 74.22 1009.52 90.93 440.32
4.83 38.44 1015.35 72.94 485.32
17.29 42.86 1014.38 72.3 464.27
8.73 36.18 1013.66 77.74 479.25
26.21 70.32 1007.0 78.29 430.4
23.72 58.62 1016.65 69.1 447.49
29.27 64.69 1006.85 55.79 438.23
10.4 40.43 1025.46 75.09 492.09
12.19 40.75 1015.13 88.98 475.36
20.4 54.9 1016.68 64.26 452.56
34.3 74.67 1015.98 25.89 427.84
27.56 68.08 1010.8 59.18 433.95
30.9 70.8 1008.48 67.48 435.27
14.85 58.59 1014.04 89.85 454.62
16.42 40.56 1020.36 50.62 472.17
16.45 63.31 1015.96 83.97 452.42
10.14 42.02 1003.19 96.51 472.17
9.53 41.44 1018.01 80.09 481.83
17.01 49.15 1021.83 84.02 458.78
23.94 62.08 1022.47 61.97 447.5
15.95 49.25 1019.04 88.51 463.4
11.15 41.26 1022.67 81.83 473.57
25.56 70.32 1009.07 90.63 433.72
27.16 66.44 1011.2 73.37 431.85
26.71 77.95 1012.13 77.5 433.47
29.56 74.22 1007.45 57.46 432.84
31.19 70.94 1007.29 51.91 436.6
6.86 41.17 1020.12 79.14 490.23
12.36 41.74 1020.58 69.24 477.16
32.82 68.31 1010.44 41.85 441.06
25.3 70.98 1007.22 95.1 440.86
8.71 41.82 1033.08 74.53 477.94
13.34 40.8 1026.56 64.85 474.47
14.2 43.02 1012.18 57.07 470.67
23.74 65.34 1013.7 62.9 447.31
16.9 44.88 1018.14 72.21 466.8
28.54 71.94 1007.4 65.99 430.91
30.15 69.88 1007.2 73.67 434.75
14.33 42.86 1010.82 88.59 469.52
25.57 59.43 1008.88 61.19 438.9
30.55 70.04 1010.51 49.37 429.56
28.04 74.33 1013.53 48.65 432.92
26.39 49.16 1005.68 56.18 442.87
15.3 41.76 1022.57 71.56 466.59
6.03 41.14 1028.04 87.46 479.61
13.49 44.63 1019.12 70.02 471.08
27.67 59.14 1016.51 61.2 433.37
24.19 65.48 1018.8 60.54 443.92
24.44 59.14 1016.74 71.82 443.5
29.86 64.79 1017.37 44.8 439.89
30.2 69.59 1008.9 67.32 434.66
7.99 41.38 1021.95 78.77 487.57
9.93 41.62 1013.76 96.02 464.64
11.03 42.32 1017.26 90.56 470.92
22.34 63.73 1014.37 83.19 444.39
25.33 48.6 1002.54 68.45 442.48
18.87 52.08 1005.25 99.19 449.61
25.97 69.34 1009.43 88.11 435.02
16.58 43.99 1021.81 79.29 458.67
14.35 46.18 1016.63 87.76 461.74
25.06 62.39 1008.09 82.56 438.31
13.85 48.92 1011.68 79.24 462.38
16.09 44.2 1019.39 67.24 460.56
26.34 59.21 1013.37 58.98 439.22
23.01 58.79 1009.71 84.22 444.64
26.39 71.25 999.8 89.12 430.34
31.32 71.29 1008.37 50.07 430.46
16.64 45.87 1009.02 98.86 456.79
13.42 41.23 994.17 95.79 468.82
20.06 44.9 1008.79 70.06 448.51
14.8 44.71 1014.67 41.71 470.77
12.59 41.14 1025.79 86.55 465.74
26.7 66.56 1005.31 71.97 430.21
19.78 50.32 1008.62 96.4 449.23
15.17 49.15 1021.91 91.73 461.89
21.71 61.45 1010.97 91.62 445.72
19.09 39.39 1013.36 59.14 466.13
19.76 51.19 1008.38 92.56 448.71
14.68 41.23 998.43 83.71 469.25
21.3 66.86 1013.04 55.43 450.56
16.73 39.64 1008.94 74.91 464.46
12.26 41.5 1014.87 89.41 471.13
14.77 48.06 1010.92 69.81 461.52
18.26 59.15 1012.04 86.01 451.09
27.1 79.74 1005.43 86.05 431.51
14.72 40.83 1009.65 80.98 469.8
26.3 51.43 1012.05 63.62 442.28
16.48 48.92 1011.84 64.16 458.67
17.99 43.79 1016.13 75.63 462.4
20.34 59.8 1015.18 80.21 453.54
25.53 62.96 1019.81 59.7 444.38
31.59 58.9 1003.39 47.6 440.52
30.8 69.14 1007.68 63.78 433.62
10.75 45.0 1023.68 89.37 481.96
19.3 44.9 1008.89 70.55 452.75
4.71 39.42 1026.4 84.42 481.28
23.1 66.05 1020.28 80.62 439.03
32.63 73.88 1005.64 52.56 435.75
26.63 74.16 1009.72 83.26 436.03
24.35 58.49 1011.03 70.64 445.6
15.11 56.03 1020.27 89.95 462.65
29.1 50.05 1005.87 51.53 438.66
21.24 50.32 1008.54 84.83 447.32
6.16 39.48 1004.85 59.68 484.55
7.36 41.01 1024.9 97.88 476.8
10.44 39.04 1023.99 85.03 480.34
26.76 48.41 1010.53 47.38 440.63
16.79 44.6 1014.27 48.08 459.48
10.76 40.43 1025.98 79.65 490.78
6.07 38.91 1019.25 83.39 483.56
27.33 73.18 1012.26 82.18 429.38
27.15 59.21 1013.49 51.71 440.27
22.35 51.43 1011.34 77.33 445.34
21.82 65.27 1013.86 72.81 447.43
21.11 69.94 1004.37 84.26 439.91
19.95 50.59 1016.11 73.23 459.27
7.45 39.61 1017.88 79.73 478.89
15.36 41.66 1012.41 62.32 466.7
15.65 43.5 1021.39 78.58 463.5
25.31 74.33 1015.04 79.88 436.21
25.88 63.47 1011.95 65.87 443.94
24.6 63.94 1012.87 80.28 439.63
22.58 41.54 1013.21 71.33 460.95
19.69 59.14 1015.99 70.33 448.69
25.85 75.08 1006.24 57.73 444.63
10.06 37.83 1005.49 99.46 473.51
18.59 39.54 1008.56 68.61 462.56
18.27 50.16 1011.07 95.91 451.76
8.85 40.43 1025.68 80.42 491.81
30.04 68.08 1011.04 51.01 429.52
26.06 49.02 1007.59 74.08 437.9
14.8 38.73 1003.18 80.73 467.54
23.93 64.45 1015.35 54.71 449.97
23.72 66.48 1003.61 73.75 436.62
11.44 40.55 1023.37 88.43 477.68
20.28 63.86 1016.04 74.66 447.26
27.9 63.13 1011.8 70.04 439.76
24.74 59.39 1015.23 74.64 437.49
14.8 58.2 1018.29 85.11 455.14
8.22 41.03 1021.76 82.97 485.5
27.56 66.93 1016.81 55.59 444.1
32.07 70.94 1006.91 49.9 432.33
9.53 44.03 1008.87 89.99 471.23
13.61 42.34 1017.93 91.61 463.89
22.2 51.19 1009.2 82.95 445.54
21.36 59.54 1007.99 92.62 446.09
23.25 63.86 1017.82 59.64 445.12
23.5 59.21 1018.29 63.0 443.31
8.46 39.66 1015.14 85.38 484.16
8.19 40.69 1019.86 85.23 477.76
30.67 71.29 1008.36 52.08 430.28
32.48 62.04 1010.39 38.05 446.48
8.99 36.66 1028.11 71.98 481.03
13.77 47.83 1007.41 90.66 466.07
19.05 67.32 1013.2 83.14 447.47
21.19 55.5 1019.83 65.22 455.93
10.12 40.0 1021.15 91.67 479.62
24.93 47.01 1014.28 66.04 455.06
8.47 40.46 1019.87 78.19 475.06
24.52 56.85 1012.59 54.47 438.89
28.55 69.84 1003.38 67.26 432.7
20.58 50.9 1011.89 72.56 452.6
18.31 46.21 1010.46 82.15 451.75
27.18 71.06 1008.16 86.32 430.66
4.43 38.91 1019.04 88.17 491.9
26.02 74.78 1010.04 72.78 439.82
15.75 39.0 1015.91 69.58 460.73
22.99 60.95 1015.14 69.86 449.7
25.52 59.15 1013.88 65.37 439.42
27.04 65.06 1013.33 52.37 439.84
6.42 35.57 1025.58 79.63 485.86
17.04 40.12 1011.81 83.14 458.1
10.79 39.82 1012.89 88.25 479.92
20.41 56.03 1019.94 55.85 458.29
7.36 40.07 1017.29 52.55 489.45
28.08 73.42 1012.17 62.74 434.0
24.74 69.13 1010.69 90.08 431.24
28.32 47.93 1003.26 54.5 439.5
16.71 40.56 1019.48 49.88 467.46
30.7 71.58 1010.0 48.96 429.27
18.42 58.95 1016.95 86.77 452.1
10.62 42.02 999.83 96.66 472.41
22.18 69.05 1002.75 70.84 442.14
22.38 49.3 1003.56 83.83 441.0
13.94 41.58 1020.76 68.22 463.07
21.24 60.84 1017.99 82.22 445.71
6.76 39.81 1017.11 87.9 483.16
26.73 68.84 1010.75 66.83 440.45
7.24 38.06 1020.6 85.36 481.83
10.84 40.62 1015.53 60.9 467.6
19.32 52.84 1004.29 83.51 450.88
29.0 69.13 1001.22 52.96 425.5
23.38 54.42 1013.95 73.02 451.87
31.17 69.51 1010.51 43.11 428.94
26.17 48.6 1002.59 61.41 439.86
30.9 73.42 1011.21 65.32 433.44
24.92 73.68 1015.12 93.68 438.23
32.77 71.32 1007.68 42.39 436.95
14.37 40.56 1021.67 68.18 470.19
8.36 40.22 1011.6 89.18 484.66
31.45 68.27 1007.56 64.79 430.81
31.6 73.17 1010.05 43.48 433.37
17.9 48.98 1014.17 80.4 453.02
20.35 50.9 1012.6 72.43 453.5
16.21 41.23 995.88 80.0 463.09
19.36 44.6 1016.25 45.65 464.56
21.04 65.46 1017.22 63.02 452.12
14.05 40.69 1015.66 74.39 470.9
23.48 64.15 1021.08 57.77 450.89
21.91 63.76 1009.85 76.8 445.04
24.42 63.07 1011.49 67.39 444.72
14.26 40.92 1022.07 73.96 460.38
21.38 58.33 1013.05 72.75 446.8
15.71 44.06 1018.34 71.69 465.05
5.78 40.62 1016.55 84.98 484.13
6.77 39.81 1017.01 87.68 488.27
23.84 49.21 1013.85 50.36 447.09
21.17 58.16 1017.16 68.11 452.02
19.94 58.96 1014.16 66.27 455.55
8.73 41.92 1029.41 89.72 480.99
16.39 41.67 1012.96 61.07 467.68

Linear Regression Model

  • Linear Regression is one of the most useful work-horses of statistical learning
  • See Chapter 7 of Kevin Murphy's Machine Learning froma Probabilistic Perspective for a good mathematical and algorithmic introduction.
  • You should have already seen Ameet's treatment of the topic from earlier notebook.
// First let's hold out 20% of our data for testing and leave 80% for training
var Array(split20, split80) = dataset.randomSplit(Array(0.20, 0.80), 1800009193L)
split20: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [AT: double, V: double ... 3 more fields]
split80: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [AT: double, V: double ... 3 more fields]
// Let's cache these datasets for performance
val testSet = split20.cache()
val trainingSet = split80.cache()
testSet: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [AT: double, V: double ... 3 more fields]
trainingSet: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [AT: double, V: double ... 3 more fields]
testSet.count() // action to actually cache
res87: Long = 1856
trainingSet.count() // action to actually cache
res88: Long = 7712

Let's take a few elements of the three DataFrames.

dataset.take(3)
res89: Array[org.apache.spark.sql.Row] = Array([14.96,41.76,1024.07,73.17,463.26], [25.18,62.96,1020.04,59.08,444.37], [5.11,39.4,1012.16,92.14,488.56])
testSet.take(3)
res90: Array[org.apache.spark.sql.Row] = Array([2.34,39.42,1028.47,69.68,490.34], [2.8,39.64,1011.01,82.96,482.66], [3.82,35.47,1016.62,84.34,489.04])
trainingSet.take(3)
res91: Array[org.apache.spark.sql.Row] = Array([1.81,39.42,1026.92,76.97,490.55], [2.58,39.42,1028.68,69.03,488.69], [2.64,39.64,1011.02,85.24,481.29])
// ***** LINEAR REGRESSION MODEL ****

import org.apache.spark.ml.regression.LinearRegression
import org.apache.spark.ml.regression.LinearRegressionModel
import org.apache.spark.ml.Pipeline

// Let's initialize our linear regression learner
val lr = new LinearRegression()
import org.apache.spark.ml.regression.LinearRegression
import org.apache.spark.ml.regression.LinearRegressionModel
import org.apache.spark.ml.Pipeline
lr: org.apache.spark.ml.regression.LinearRegression = linReg_3b8dffe4015f
// We use explain params to dump the parameters we can use
lr.explainParams()
res92: String =
aggregationDepth: suggested depth for treeAggregate (>= 2) (default: 2)
elasticNetParam: the ElasticNet mixing parameter, in range [0, 1]. For alpha = 0, the penalty is an L2 penalty. For alpha = 1, it is an L1 penalty (default: 0.0)
epsilon: The shape parameter to control the amount of robustness. Must be > 1.0. (default: 1.35)
featuresCol: features column name (default: features)
fitIntercept: whether to fit an intercept term (default: true)
labelCol: label column name (default: label)
loss: The loss function to be optimized. Supported options: squaredError, huber. (Default squaredError) (default: squaredError)
maxIter: maximum number of iterations (>= 0) (default: 100)
predictionCol: prediction column name (default: prediction)
regParam: regularization parameter (>= 0) (default: 0.0)
solver: The solver algorithm for optimization. Supported options: auto, normal, l-bfgs. (Default auto) (default: auto)
standardization: whether to standardize the training features before fitting the model (default: true)
tol: the convergence tolerance for iterative algorithms (>= 0) (default: 1.0E-6)
weightCol: weight column name. If this is not set or empty, we treat all instance weights as 1.0 (undefined)

The cell below is based on the Spark ML pipeline API. More information can be found in the Spark ML Programming Guide at https://spark.apache.org/docs/latest/ml-guide.html

// Now we set the parameters for the method
lr.setPredictionCol("Predicted_PE")
  .setLabelCol("PE")
  .setMaxIter(100)
  .setRegParam(0.1)
// We will use the new spark.ml pipeline API. If you have worked with scikit-learn this will be very familiar.
val lrPipeline = new Pipeline()
lrPipeline.setStages(Array(vectorizer, lr))
// Let's first train on the entire dataset to see what we get
val lrModel = lrPipeline.fit(trainingSet)
lrPipeline: org.apache.spark.ml.Pipeline = pipeline_07136143d91d
lrModel: org.apache.spark.ml.PipelineModel = pipeline_07136143d91d

Since Linear Regression is simply a line of best fit over the data that minimizes the square of the error, given multiple input dimensions we can express each predictor as a line function of the form:

\[ y = b_0 + b_1 x_1 + b_2 x_2 + b_3 x_3 + \ldots + b_i x_i + \ldots + b_k x_k \]

where \(b_0\) is the intercept and \(b_i\)'s are coefficients.

To express the coefficients of that line we can retrieve the Estimator stage from the fitted, linear-regression pipeline model named lrModel and express the weights and the intercept for the function.

// The intercept is as follows:
val intercept = lrModel.stages(1).asInstanceOf[LinearRegressionModel].intercept
intercept: Double = 434.0183482461227
// The coefficents (i.e. weights) are as follows:

val weights = lrModel.stages(1).asInstanceOf[LinearRegressionModel].coefficients.toArray
weights: Array[Double] = Array(-1.9288465830313846, -0.24931659465920197, 0.08140785421485836, -0.1458797521995801)

The model has been fit and the intercept and coefficients displayed above.

Now, let us do some work to make a string of the model that is easy to understand for an applied data scientist or data analyst.

val featuresNoLabel = dataset.columns.filter(col => col != "PE")
featuresNoLabel: Array[String] = Array(AT, V, AP, RH)
val coefficentFeaturePairs = sc.parallelize(weights).zip(sc.parallelize(featuresNoLabel))
coefficentFeaturePairs: org.apache.spark.rdd.RDD[(Double, String)] = ZippedPartitionsRDD2[32671] at zip at command-2972105651606305:1
coefficentFeaturePairs.collect() // this just pairs each coefficient with the name of its corresponding feature
res93: Array[(Double, String)] = Array((-1.9288465830313846,AT), (-0.24931659465920197,V), (0.08140785421485836,AP), (-0.1458797521995801,RH))
// Now let's sort the coefficients from the largest to the smallest

var equation = s"y = $intercept "
//var variables = Array
coefficentFeaturePairs.sortByKey().collect().foreach({
  case (weight, feature) =>
  { 
        val symbol = if (weight > 0) "+" else "-"
        val absWeight = Math.abs(weight)
        equation += (s" $symbol (${absWeight} * ${feature})")
  }
}
)
equation: String = y = 434.0183482461227  - (1.9288465830313846 * AT) - (0.24931659465920197 * V) - (0.1458797521995801 * RH) + (0.08140785421485836 * AP)
// Finally here is our equation
println("Linear Regression Equation: " + equation)
Linear Regression Equation: y = 434.0183482461227  - (1.9288465830313846 * AT) - (0.24931659465920197 * V) - (0.1458797521995801 * RH) + (0.08140785421485836 * AP)

Based on examining the fitted Linear Regression Equation above:

  • There is a strong negative correlation between Atmospheric Temperature (AT) and Power Output due to the coefficient being greater than -1.91.
  • But our other dimenensions seem to have little to no correlation with Power Output.

Do you remember Step 2: Explore Your Data? When we visualized each predictor against Power Output using a Scatter Plot, only the temperature variable seemed to have a linear correlation with Power Output so our final equation seems logical.

Now let's see what our predictions look like given this model.

val predictionsAndLabels = lrModel.transform(testSet)

display(predictionsAndLabels.select("AT", "V", "AP", "RH", "PE", "Predicted_PE"))
AT V AP RH PE Predicted_PE
2.34 39.42 1028.47 69.68 490.34 493.23742177145215
2.8 39.64 1011.01 82.96 482.66 488.93663844863084
3.82 35.47 1016.62 84.34 489.04 488.2642491377776
3.98 35.47 1017.22 86.53 489.64 487.68500173970443
4.23 38.44 1016.46 76.64 489.0 487.8432005878593
4.32 35.47 1017.8 88.51 488.03 486.7875685475632
4.43 38.91 1019.04 88.17 491.9 485.8682911927764
4.65 35.19 1018.23 94.78 489.36 485.34119715268844
4.78 42.85 1013.39 93.36 481.47 482.9938172155284
4.87 42.85 1012.69 94.72 482.05 482.5648390621137
4.96 40.07 1011.8 67.38 494.75 487.00024243767876
4.97 42.85 1014.02 88.78 482.98 483.3467525779819
5.01 39.4 1003.69 91.9 475.34 482.8336530053327
5.06 40.64 1021.49 93.7 483.73 483.6145343498689
5.15 35.19 1018.63 93.94 488.42 484.53187599470635
5.15 40.07 1012.27 63.31 495.35 487.2657538698361
5.17 35.57 1026.68 79.86 491.32 487.10787889447494
5.21 41.31 1003.51 91.23 486.46 482.0547750131424
5.23 40.78 1025.13 92.74 483.12 483.688095258955
5.25 40.07 1019.48 67.7 495.23 487.0194077282659
5.28 45.87 1008.25 97.88 479.91 480.1986449575354
5.29 41.38 1020.62 83.83 492.12 484.35541367676683
5.42 41.38 1020.77 86.02 491.38 483.7973981417879
5.47 40.62 1018.66 83.61 481.56 484.07023605498495
5.51 41.03 1022.28 84.5 491.84 484.05572584065357
5.53 35.79 1011.19 94.01 484.64 483.0334383183464
5.54 41.38 1020.47 82.91 490.07 483.9952002249004
5.54 45.87 1008.69 95.91 478.02 480.02034741363497
5.56 45.87 1006.99 96.48 476.61 479.7602256710553
5.65 40.72 1022.46 85.17 487.09 483.7798894431585
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21.44 63.09 1016.56 90.11 444.19 446.545237358833
21.45 45.09 1013.83 52.26 453.15 456.3129527756159
21.45 60.08 1017.92 72.7 451.49 449.9268730104538
21.45 66.05 1014.81 73.73 453.38 448.0350183689646
21.46 46.63 1012.97 71.29 452.1 453.06361431502756
21.47 58.79 1017.0 76.97 446.33 449.51211271813366
21.49 56.9 1007.47 66.66 452.46 450.672947544889
21.52 66.51 1015.32 72.85 444.87 447.9552056621943
21.53 52.84 1005.06 88.22 444.04 448.2666586698033
21.54 58.49 1010.85 78.9 449.12 448.66968221055265
21.54 69.48 1011.04 80.48 443.15 445.7146703190735
21.55 44.57 1006.03 71.54 446.84 452.8021698612517
21.55 60.27 1017.42 92.59 443.93 446.7443660008083
21.57 66.49 1014.76 68.19 455.18 448.49796091182566
21.58 63.87 1015.27 63.15 451.88 449.90863388073797
21.61 41.54 1014.5 75.62 458.47 453.53620348431275
21.61 49.39 1019.41 78.2 449.26 451.60241101975805
21.62 50.05 1007.2 92.9 444.16 448.28015134415546
21.65 58.18 1008.33 95.28 441.05 445.940139097113
21.69 44.57 1005.84 71.53 447.88 452.5181226448485
21.71 65.27 1013.24 63.58 444.91 449.080854354919
21.73 69.05 1001.31 86.64 439.01 443.764677908941
21.75 59.8 1016.65 72.94 453.17 449.2796285666682

Now that we have real predictions we can use an evaluation metric such as Root Mean Squared Error to validate our regression model. The lower the Root Mean Squared Error, the better our model.

//Now let's compute some evaluation metrics against our test dataset

import org.apache.spark.mllib.evaluation.RegressionMetrics 

val metrics = new RegressionMetrics(predictionsAndLabels.select("Predicted_PE", "PE").rdd.map(r => (r(0).asInstanceOf[Double], r(1).asInstanceOf[Double])))
import org.apache.spark.mllib.evaluation.RegressionMetrics
metrics: org.apache.spark.mllib.evaluation.RegressionMetrics = org.apache.spark.mllib.evaluation.RegressionMetrics@2cb97126
val rmse = metrics.rootMeanSquaredError
rmse: Double = 4.426730543741181
val explainedVariance = metrics.explainedVariance
explainedVariance: Double = 269.3177257387032
val r2 = metrics.r2
r2: Double = 0.9314313152952873
println (f"Root Mean Squared Error: $rmse")
println (f"Explained Variance: $explainedVariance")  
println (f"R2: $r2")
Root Mean Squared Error: 4.426730543741181
Explained Variance: 269.3177257387032
R2: 0.9314313152952873

Generally a good model will have 68% of predictions within 1 RMSE and 95% within 2 RMSE of the actual value. Let's calculate and see if our RMSE meets this criteria.

display(predictionsAndLabels) // recall the DataFrame predictionsAndLabels
// First we calculate the residual error and divide it by the RMSE from predictionsAndLabels DataFrame and make another DataFrame that is registered as a temporary table Power_Plant_RMSE_Evaluation
predictionsAndLabels.selectExpr("PE", "Predicted_PE", "PE - Predicted_PE AS Residual_Error", s""" (PE - Predicted_PE) / $rmse AS Within_RSME""").createOrReplaceTempView("Power_Plant_RMSE_Evaluation")
SELECT * from Power_Plant_RMSE_Evaluation
PE Predicted_PE Residual_Error Within_RSME
490.34 493.23742177145215 -2.897421771452173 -0.6545286058914855
482.66 488.93663844863084 -6.27663844863082 -1.4178948518800556
489.04 488.2642491377776 0.7757508622224236 0.17524239493619823
489.64 487.68500173970443 1.9549982602955538 0.44163480044197995
489.0 487.8432005878593 1.1567994121406855 0.26132139752130357
488.03 486.7875685475632 1.24243145243679 0.28066570579802425
491.9 485.8682911927764 6.031708807223595 1.3625651590092023
489.36 485.34119715268844 4.018802847311576 0.9078489886839033
481.47 482.9938172155284 -1.5238172155283678 -0.3442308494884213
482.05 482.5648390621137 -0.5148390621137082 -0.11630232674577932
494.75 487.00024243767876 7.749757562321236 1.7506729821805804
482.98 483.3467525779819 -0.3667525779818561 -8.284953745386567e-2
475.34 482.8336530053327 -7.493653005332703 -1.692818871916148
483.73 483.6145343498689 0.11546565013111376 2.608373132048146e-2
488.42 484.53187599470635 3.888124005293662 0.8783285919200484
495.35 487.2657538698361 8.084246130163933 1.8262340682999108
491.32 487.10787889447494 4.212121105525057 0.9515196517846441
486.46 482.0547750131424 4.405224986857604 0.9951418870719423
483.12 483.688095258955 -0.5680952589549975 -0.12833292050229034
495.23 487.0194077282659 8.210592271734129 1.8547757064958097
479.91 480.1986449575354 -0.2886449575353822 -6.520499829010114e-2
492.12 484.35541367676683 7.764586323233175 1.7540228045303743
491.38 483.7973981417879 7.582601858212115 1.712912449331917
481.56 484.07023605498495 -2.5102360549849436 -0.567063215206105
491.84 484.05572584065357 7.78427415934641 1.758470293691663
484.64 483.0334383183464 1.6065616816536021 0.36292285373571487
490.07 483.9952002249004 6.0747997750996205 1.3722994239368362
478.02 480.02034741363497 -2.0003474136349837 -0.4518791902667791
476.61 479.7602256710553 -3.1502256710552956 -0.711637096481805
487.09 483.7798894431585 3.3101105568414937 0.7477551488923485
482.82 483.2217349280458 -0.401734928045812 -9.075206274161249e-2
481.6 480.1171178824119 1.482882117588133 0.33498359634397323
470.02 482.0478125504672 -12.027812550467218 -2.717087121436152
489.05 481.81327159305386 7.236728406946156 1.6347795140090344
487.03 484.6333949755666 2.39660502443337 0.5413939250993844
490.57 482.2826790358646 8.287320964135404 1.8721087453250556
488.57 482.86050781997415 5.709492180025848 1.2897763086344445
480.39 483.17821215232124 -2.7882121523212504 -0.6298581141929721
481.37 483.0829476732433 -1.7129476732433204 -0.3869554869711247
489.62 482.71830544679335 6.901694553206653 1.5590952476122018
481.13 481.35862683823984 -0.22862683823984753 -5.164688385271067e-2
485.94 481.4164995749685 4.5235004250315 1.021860350507925
482.49 482.3037528502627 0.18624714973731216 4.2073297187840204e-2
483.77 483.6070229944035 0.1629770055964741 3.6816563372465104e-2
491.77 481.0249164343975 10.7450835656025 2.4273181887690556
483.43 482.2081944229683 1.2218055770317164 0.2760063132279849
481.49 482.6905244198958 -1.2005244198957712 -0.2711988922825122
478.78 480.9741288614041 -2.194128861404124 -0.49565448805243767
492.96 485.8565717694332 7.103428230566806 1.6046669568831393
481.36 483.99243959507345 -2.6324395950734356 -0.5946690382578993
486.68 481.76650494734884 4.913495052651172 1.1099602752189677
484.94 483.069724719673 1.8702752803270073 0.42249584921569994
483.01 481.33834961288795 1.671650387112038 0.3776264153858503
488.17 483.1883946104104 4.9816053895896175 1.1253464244922151
490.41 480.1679106982307 10.24208930176934 2.313691606156222
483.11 482.4149038683481 0.6950961316518942 0.15702246269194528
485.89 480.94068220101354 4.949317798986442 1.1180526463224945
487.08 482.508645049916 4.571354950083958 1.0326707046913566
477.8 480.01746628251317 -2.2174662825131577 -0.5009264197587914
489.96 480.63940670945976 9.320593290540216 2.1055253303633577
486.92 483.0108446487773 3.9091553512226938 0.883079580425271
486.37 482.57972730795177 3.7902726920482337 0.8562239455498787
488.2 483.51586402481416 4.684135975185825 1.0581479782654901
479.06 481.6634377951154 -2.603437795115383 -0.5881175213603873
480.05 484.68450470880435 -4.634504708804343 -1.0469362575856187
487.18 482.8218608903564 4.358139109643616 0.9845051707078616
480.47 481.8880244206695 -1.4180244206694965 -0.32033221960491765
480.36 480.6306788292839 -0.2706788292838951 -6.11464435454739e-2
487.85 479.89671820679695 7.953281793203075 1.7966491781271794
486.11 479.6914116057231 6.418588394276924 1.449961394951398
481.83 481.1970697561745 0.6329302438254558 0.1429791665816065
482.96 482.17217802621536 0.7878219737846166 0.17796926331974147
483.92 481.3074409763495 2.612559023650533 0.590178010121793
477.69 479.64992318380445 -1.9599231838044489 -0.4427473424095181
474.25 480.70714895561014 -6.457148955610137 -1.4586722394340677
479.08 479.7024675196716 -0.6224675196716021 -0.14061563348410486
478.89 481.00544489343537 -2.115444893435381 -0.4778797517789611
483.11 482.38901084355183 0.7209891564481836 0.16287170617772706
488.43 481.25646633043965 7.173533669560356 1.6205038004183012
483.28 480.33371483717946 2.946285162820516 0.6655668633335223
486.76 482.5311759738776 4.228824026122368 0.9552928474721311
476.58 480.67721106043905 -4.097211060439065 -0.9255614318409298
481.61 482.53257783094546 -0.9225778309454427 -0.20841065925050425
477.8 480.0330510466423 -2.233051046642288 -0.5044470235035043
475.32 479.3324132109004 -4.012413210900434 -0.9064055675522111
475.89 478.2499419685471 -2.359941968547105 -0.5331117277702286
485.03 480.3355565472517 4.69444345274826 1.0604764411029242
482.46 479.7315598782737 2.728440121726294 0.6163555912803304
484.57 477.91894784424176 6.6510521557582365 1.502475041125319
483.94 483.45191519870116 0.48808480129883947 0.11025852973791857
482.39 482.34452319301437 4.547680698561862e-2 1.027322682875218e-2
483.8 478.45760011663003 5.342399883369978 1.2068500286116204
482.22 478.7638216096892 3.4561783903108108 0.7807519242835766
481.52 479.1388800137473 2.3811199862526564 0.5378958494817917
483.79 477.1846287648614 6.605371235138648 1.4921557049542535
480.54 476.81117998099177 3.7288200190082534 0.8423417649127792
477.27 480.84424359067077 -3.5742435906707897 -0.8074228949228237
474.5 480.1364995691749 -5.636499569174873 -1.273287251952606
475.52 479.2235127059344 -3.703512705934429 -0.8366248339128552
481.44 478.91505388939413 2.5249461106058675 0.5703862219885535
480.6 476.210862698602 4.389137301398023 0.9915076732202934
487.19 481.0254321330136 6.164567866986374 1.392578067734949
475.42 480.36098930984286 -4.940989309842848 -1.1161712376708273
476.22 478.51210495606927 -2.292104956069238 -0.5177873225895746
485.13 479.57731721621883 5.552682783781165 1.2543530104022107
488.02 484.33140555054337 3.688594449456616 0.8332547944829863
477.78 478.4450809561189 -0.6650809561189135 -0.15024202389261102
477.2 480.5031526805204 -3.303152680520384 -0.7461833621634392
467.56 479.2169410835439 -11.65694108354387 -2.6333071255094267
485.18 477.6146348725092 7.565365127490793 1.7090186657480726
483.52 478.33312476559934 5.186875234400645 1.17171695524459
480.21 479.4778900760471 0.7321099239528621 0.16538389150158914
478.81 481.48536176155926 -2.675361761559259 -0.6043651708916123
484.67 477.9675154808001 6.702484519199913 1.5140936302699408
477.9 479.6817134321857 -1.781713432185711 -0.40248969630754267
475.17 477.5050067316079 -2.335006731607905 -0.5274788489010923
485.73 478.32045063849523 7.409549361504787 1.673819828943716
479.91 478.1399555772117 1.7700444227883168 0.3998536629456538
486.4 479.65037308403333 6.749626915966644 1.5247431144210337
480.15 477.1324329554068 3.017567044593193 0.681669465709775
480.58 482.82343628916425 -2.243436289164265 -0.5067930534728822
484.07 478.16947013024355 5.90052986975644 1.3329317905059794
481.89 480.6437911412516 1.246208858748389 0.2815190232236669
483.14 478.8928744938167 4.247125506183295 0.9594271583094607
479.31 476.1246111330079 3.1853888669921275 0.7195804749163808
484.21 477.288235770853 6.921764229146959 1.563628994525865
476.02 478.30600580479216 -2.2860058047921825 -0.5164095221527084
480.69 478.2957350932866 2.3942649067133743 0.5408652916763936
481.91 476.52270993699136 5.387290063008663 1.2169907361146226
485.06 478.99917896902446 6.060821030975546 1.3691416206809235
485.29 480.8674382556021 4.42256174439791 0.9990582667496749
482.39 481.1210453702997 1.2689546297002607 0.2866573009496584
478.25 478.8354389662744 -0.5854389662744097 -0.1322508701375881
475.79 476.29244393984663 -0.5024439398466143 -0.11350226422907182
485.87 479.0178844308566 6.852115569143393 1.5478953375265612
479.23 476.4582419334783 2.771758066521727 0.6261411303745675
478.61 480.1903466285615 -1.5803466285614718 -0.3570008639436786
479.94 479.4487267515188 0.4912732484812068 0.11097880108736301
479.25 479.3384367489267 -8.84367489267106e-2 -1.997789295120947e-2
480.99 477.44189376811596 3.5481062318840486 0.8015184563019332
481.07 476.33561360755584 4.734386392444151 1.0694995653480546
480.4 482.3769169335795 -1.9769169335795027 -0.44658623651141477
482.8 476.04420182940044 6.755798170599576 1.5261372030315674
480.08 479.65335282852305 0.42664717147692954 9.637974736911713e-2
475.0 478.6696951676176 -3.66969516761759 -0.8289854400119429
483.88 476.696926422392 7.183073577608013 1.6226588690300885
482.52 476.90393713153463 5.616062868465349 1.2686705940133918
478.45 479.2188844607746 -0.7688844607745864 -0.17369127241360752
482.3 475.81261283946816 6.487387160531853 1.465503060651426
472.45 476.2100211409317 -3.7600211409317126 -0.8493901094223798
480.2 480.2141595165933 -1.415951659333814e-2 -3.19863982083975e-3
478.38 474.9481764100585 3.431823589941473 0.775250166241454
472.77 479.30598211413803 -6.535982114138051 -1.476480677907779
483.53 476.3744577455605 7.155542254439467 1.6164395333609067
475.47 478.6980048877349 -3.228004887734869 -0.7292074491181413
467.24 476.41215657483474 -9.17215657483473 -2.0719934236347326
481.03 480.7338755379764 0.29612446202355613 6.689462100697262e-2
482.37 480.51130475015583 1.8586952498441747 0.41987991622217147
484.97 478.0206284049 6.949371595100047 1.5698655082870474
479.53 475.4980717304681 4.031928269531875 0.9108140262190783
482.8 476.4769333498689 6.323066650131125 1.4283829990671366
477.26 480.5658974037096 -3.3058974037095936 -0.7468033961054397
479.02 478.9378167534134 8.218324658656684e-2 1.8565224554443056e-2
476.69 479.483969889582 -2.7939698895820015 -0.631158789082455
476.62 476.72728884411293 -0.10728884411292938 -2.423658794064658e-2
475.69 475.1283411969007 0.5616588030993057 0.1268789228414677
482.95 477.43108128919135 5.518918710808634 1.2467256943415417
483.24 479.0201634085648 4.2198365914351825 0.9532625827884375
484.86 476.63324412261045 8.226755877389564 1.858427070746631
491.97 478.3337308000573 13.636269199942717 3.080438049074982
474.88 478.39283560851754 -3.5128356085175483 -0.7935508099728905
475.64 477.10087603877 -1.4608760387700386 -0.33001241533337206
484.96 478.16396362897893 6.796036371021046 1.5352270267793358
475.42 478.96772021173297 -3.547720211732951 -0.8014312542128782
480.38 475.6006326388746 4.7793673611254235 1.0796607821279804
478.82 474.9766634864767 3.8433365135232975 0.8682110816429235
482.55 478.786077505979 3.763922494021017 0.8502714264690703
480.14 478.9365615888623 1.2034384111377108 0.271857163937664
482.55 476.1723094438278 6.377690556172183 1.4407225588170043
477.91 478.2490255806092 -0.33902558060918864 -7.658599891256687e-2
476.25 474.4577268339357 1.7922731660643194 0.4048751439362759
471.13 478.43777544278043 -7.307775442780439 -1.6508290646045036
482.16 478.00197412694763 4.158025873052395 0.9392995195813987
480.87 479.3152324207446 1.5547675792553832 0.3512225476325008
477.34 477.2801935898294 5.980641017055177e-2 1.3510289270963245e-2
483.66 478.285031656868 5.374968343132025 1.214207255223955
481.95 475.9420528274367 6.007947172563263 1.357197397311141
479.68 476.17198214059135 3.5080178594086533 0.7924624787403274
478.66 474.34503134979343 4.314968650206595 0.9747529486084029
478.8 479.7691576930105 -0.9691576930105157 -0.2189330666129607
481.12 475.82678857769963 5.293211422300374 1.1957383378087658
476.54 478.0366119605891 -1.496611960589064 -0.33808517274788225
478.03 477.46151999839185 0.5684800016081226 0.12841983400410018
479.23 479.110912113517 0.1190878864830438 2.6901995797195863e-2
480.74 477.72481326338215 3.0151867366178635 0.6811317532938489
478.88 479.54303529435083 -0.6630352943508342 -0.14977990817360218
481.05 479.71268358186353 1.3373164181364814 0.3021002532054435
473.54 473.26068816423447 0.2793118357655544 6.309664277182285e-2
469.73 476.05175958076205 -6.321759580762034 -1.4280877316330394
475.51 476.88388448180046 -1.3738844818004736 -0.31036099175789383
476.67 475.61433131158714 1.0556686884128794 0.23847593115995214
472.16 477.7130066863276 -5.553006686327592 -1.2544261801023373
481.85 475.2673812565115 6.582618743488524 1.487015909020143
479.45 479.3846135509556 6.538644904441071e-2 1.4770822031817277e-2
482.38 475.5344685772051 6.84553142279492 1.5464079765310332
469.58 473.85672752722735 -4.276727527227365 -0.9661142653632034
477.93 477.3826135030455 0.5473864969545161 0.12365480382094843
478.21 477.2300569616709 0.9799430383290542 0.2213694799459989
477.62 479.265495182268 -1.6454951822680073 -0.371717945334288
472.46 472.7773808573311 -0.3173808573311021 -7.16964482466269e-2
467.37 473.2887424901299 -5.918742490129887 -1.3370460279083884
473.2 475.32128019247375 -2.121280192473762 -0.4791979479015218
480.05 476.83702080523557 3.2129791947644435 0.7258131397464832
469.65 473.90133694043874 -4.251336940438762 -0.9603785228015735
485.23 477.4312500724956 7.798749927504446 1.761740374853143
477.88 474.53026960482526 3.3497303951747313 0.756705284425051
475.21 475.5632280329792 -0.35322803297924565 -7.97943379405968e-2
475.91 476.45899184845075 -0.5489918484507257 -0.12401745329336308
477.85 475.16451288467897 2.6854871153210524 0.6066524918978817
464.86 472.95056743270436 -8.090567432704347 -1.827662052785967
466.05 473.09691475779204 -7.046914757792024 -1.591900543337891
463.16 472.93274352761154 -9.77274352761151 -2.2076662292962226
475.75 478.4561215361668 -2.7061215361667905 -0.6113138148859982
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439.01 443.764677908941 -4.754677908941005 -1.0740834261221295
453.17 449.2796285666682 3.890371433331836 0.8788362867110385
-- Now we can display the RMSE as a Histogram. Clearly this shows that the RMSE is centered around 0 with the vast majority of the error within 2 RMSEs.
SELECT Within_RSME  from Power_Plant_RMSE_Evaluation
Within_RSME
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We can see this definitively if we count the number of predictions within + or - 1.0 and + or - 2.0 and display this as a pie chart:

SELECT case when Within_RSME <= 1.0 and Within_RSME >= -1.0 then 1  when  Within_RSME <= 2.0 and Within_RSME >= -2.0 then 2 else 3 end RSME_Multiple, COUNT(*) count  from Power_Plant_RMSE_Evaluation
group by case when Within_RSME <= 1.0 and Within_RSME >= -1.0 then 1  when  Within_RSME <= 2.0 and Within_RSME >= -2.0 then 2 else 3 end
RSME_Multiple count
1.0 1267.0
3.0 77.0
2.0 512.0

So we have about 70% of our training data within 1 RMSE and about 97% (70% + 27%) within 2 RMSE. So the model is pretty decent. Let's see if we can tune the model to improve it further.

NOTE: these numbers will vary across runs due to the seed in random sampling of training and test set, number of iterations, and other stopping rules in optimization, for example.

Step 7: Tuning and Evaluation

Now that we have a model with all of the data let's try to make a better model by tuning over several parameters.

import org.apache.spark.ml.tuning.{ParamGridBuilder, CrossValidator}
import org.apache.spark.ml.evaluation._
import org.apache.spark.ml.tuning.{ParamGridBuilder, CrossValidator}
import org.apache.spark.ml.evaluation._

First let's use a cross validator to split the data into training and validation subsets. See http://spark.apache.org/docs/latest/ml-tuning.html.

//Let's set up our evaluator class to judge the model based on the best root mean squared error
val regEval = new RegressionEvaluator()
regEval.setLabelCol("PE")
  .setPredictionCol("Predicted_PE")
  .setMetricName("rmse")
regEval: org.apache.spark.ml.evaluation.RegressionEvaluator = RegressionEvaluator: uid=regEval_c75f9d66a6cb, metricName=rmse, throughOrigin=false
res101: regEval.type = RegressionEvaluator: uid=regEval_c75f9d66a6cb, metricName=rmse, throughOrigin=false

We now treat the lrPipeline as an Estimator, wrapping it in a CrossValidator instance.

This will allow us to jointly choose parameters for all Pipeline stages.

A CrossValidator requires an Estimator, an Evaluator (which we set next).

//Let's create our crossvalidator with 3 fold cross validation
val crossval = new CrossValidator()
crossval.setEstimator(lrPipeline)
crossval.setNumFolds(3)
crossval.setEvaluator(regEval)
crossval: org.apache.spark.ml.tuning.CrossValidator = cv_bc136566b6a6
res102: crossval.type = cv_bc136566b6a6

A CrossValidator also requires a set of EstimatorParamMaps which we set next.

For this we need a regularization parameter (more generally a hyper-parameter that is model-specific).

Now, let's tune over our regularization parameter from 0.01 to 0.10.

val regParam = ((1 to 10) toArray).map(x => (x /100.0))
warning: there was one feature warning; for details, enable `:setting -feature' or `:replay -feature'
regParam: Array[Double] = Array(0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1)

Check out the scala docs for syntactic details on org.apache.spark.ml.tuning.ParamGridBuilder.

val paramGrid = new ParamGridBuilder()
                    .addGrid(lr.regParam, regParam)
                    .build()
crossval.setEstimatorParamMaps(paramGrid)
paramGrid: Array[org.apache.spark.ml.param.ParamMap] =
Array({
	linReg_3b8dffe4015f-regParam: 0.01
}, {
	linReg_3b8dffe4015f-regParam: 0.02
}, {
	linReg_3b8dffe4015f-regParam: 0.03
}, {
	linReg_3b8dffe4015f-regParam: 0.04
}, {
	linReg_3b8dffe4015f-regParam: 0.05
}, {
	linReg_3b8dffe4015f-regParam: 0.06
}, {
	linReg_3b8dffe4015f-regParam: 0.07
}, {
	linReg_3b8dffe4015f-regParam: 0.08
}, {
	linReg_3b8dffe4015f-regParam: 0.09
}, {
	linReg_3b8dffe4015f-regParam: 0.1
})
res103: crossval.type = cv_bc136566b6a6
//Now let's create our model
val cvModel = crossval.fit(trainingSet)
cvModel: org.apache.spark.ml.tuning.CrossValidatorModel = CrossValidatorModel: uid=cv_bc136566b6a6, bestModel=pipeline_07136143d91d, numFolds=3

In addition to CrossValidator Spark also offers TrainValidationSplit for hyper-parameter tuning. TrainValidationSplit only evaluates each combination of parameters once as opposed to k times in case of CrossValidator. It is therefore less expensive, but will not produce as reliable results when the training dataset is not sufficiently large.

Now that we have tuned let's see what we got for tuning parameters and what our RMSE was versus our intial model

val predictionsAndLabels = cvModel.transform(testSet)
val metrics = new RegressionMetrics(predictionsAndLabels.select("Predicted_PE", "PE").rdd.map(r => (r(0).asInstanceOf[Double], r(1).asInstanceOf[Double])))

val rmse = metrics.rootMeanSquaredError
val explainedVariance = metrics.explainedVariance
val r2 = metrics.r2
predictionsAndLabels: org.apache.spark.sql.DataFrame = [AT: double, V: double ... 5 more fields]
metrics: org.apache.spark.mllib.evaluation.RegressionMetrics = org.apache.spark.mllib.evaluation.RegressionMetrics@671c9416
rmse: Double = 4.4286032895695895
explainedVariance: Double = 271.5750243564875
r2: Double = 0.9313732865178349
println (f"Root Mean Squared Error: $rmse")
println (f"Explained Variance: $explainedVariance")  
println (f"R2: $r2")
Root Mean Squared Error: 4.4286032895695895
Explained Variance: 271.5750243564875
R2: 0.9313732865178349

So our initial untuned and tuned linear regression models are statistically identical.

Given that the only linearly correlated variable is Temperature, it makes sense try another machine learning method such a Decision Tree to handle non-linear data and see if we can improve our model

A Decision Tree creates a model based on splitting variables using a tree structure. We will first start with a single decision tree model.

Reference Decision Trees: https://en.wikipedia.org/wiki/Decisiontreelearning

//Let's build a decision tree pipeline
import org.apache.spark.ml.regression.DecisionTreeRegressor

// we are using a Decision Tree Regressor as opposed to a classifier we used for the hand-written digit classification problem
val dt = new DecisionTreeRegressor()
dt.setLabelCol("PE")
dt.setPredictionCol("Predicted_PE")
dt.setFeaturesCol("features")
dt.setMaxBins(100)

val dtPipeline = new Pipeline()
dtPipeline.setStages(Array(vectorizer, dt))
import org.apache.spark.ml.regression.DecisionTreeRegressor
dt: org.apache.spark.ml.regression.DecisionTreeRegressor = dtr_92691f930484
dtPipeline: org.apache.spark.ml.Pipeline = pipeline_ddfeb1cfff04
res106: dtPipeline.type = pipeline_ddfeb1cfff04
//Let's just resuse our CrossValidator
crossval.setEstimator(dtPipeline)
res107: crossval.type = cv_bc136566b6a6
val paramGrid = new ParamGridBuilder()
                     .addGrid(dt.maxDepth, Array(2, 3))
                     .build()
paramGrid: Array[org.apache.spark.ml.param.ParamMap] =
Array({
	dtr_92691f930484-maxDepth: 2
}, {
	dtr_92691f930484-maxDepth: 3
})
crossval.setEstimatorParamMaps(paramGrid)
res108: crossval.type = cv_bc136566b6a6
val dtModel = crossval.fit(trainingSet) // fit decitionTree with cv
dtModel: org.apache.spark.ml.tuning.CrossValidatorModel = CrossValidatorModel: uid=cv_bc136566b6a6, bestModel=pipeline_ddfeb1cfff04, numFolds=3
import org.apache.spark.ml.regression.DecisionTreeRegressionModel
import org.apache.spark.ml.PipelineModel
dtModel.bestModel.asInstanceOf[PipelineModel].stages.last.asInstanceOf[DecisionTreeRegressionModel].toDebugString
import org.apache.spark.ml.regression.DecisionTreeRegressionModel
import org.apache.spark.ml.PipelineModel
res109: String =
"DecisionTreeRegressionModel: uid=dtr_92691f930484, depth=3, numNodes=15, numFeatures=4
  If (feature 0 <= 18.595)
   If (feature 0 <= 11.885000000000002)
    If (feature 0 <= 8.575)
     Predict: 483.994943457189
    Else (feature 0 > 8.575)
     Predict: 476.04374262101527
   Else (feature 0 > 11.885000000000002)
    If (feature 0 <= 15.475000000000001)
     Predict: 467.5564649956784
    Else (feature 0 > 15.475000000000001)
     Predict: 459.5010376134889
  Else (feature 0 > 18.595)
   If (feature 1 <= 66.21000000000001)
    If (feature 0 <= 22.055)
     Predict: 452.01076923076914
    Else (feature 0 > 22.055)
     Predict: 443.46937926330156
   Else (feature 1 > 66.21000000000001)
    If (feature 0 <= 25.325)
     Predict: 440.73731707317074
    Else (feature 0 > 25.325)
     Predict: 433.86131215469624
"

The line above will pull the Decision Tree model from the Pipeline and display it as an if-then-else string.

Next let's visualize it as a decision tree for regression.

display(dtModel.bestModel.asInstanceOf[PipelineModel].stages.last.asInstanceOf[DecisionTreeRegressionModel])
treeNode
{"index":7,"featureType":"continuous","prediction":null,"threshold":18.595,"categories":null,"feature":0,"overflow":false}
{"index":3,"featureType":"continuous","prediction":null,"threshold":11.885000000000002,"categories":null,"feature":0,"overflow":false}
{"index":1,"featureType":"continuous","prediction":null,"threshold":8.575,"categories":null,"feature":0,"overflow":false}
{"index":0,"featureType":null,"prediction":483.994943457189,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":2,"featureType":null,"prediction":476.04374262101527,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":5,"featureType":"continuous","prediction":null,"threshold":15.475000000000001,"categories":null,"feature":0,"overflow":false}
{"index":4,"featureType":null,"prediction":467.5564649956784,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":6,"featureType":null,"prediction":459.5010376134889,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":11,"featureType":"continuous","prediction":null,"threshold":66.21000000000001,"categories":null,"feature":1,"overflow":false}
{"index":9,"featureType":"continuous","prediction":null,"threshold":22.055,"categories":null,"feature":0,"overflow":false}
{"index":8,"featureType":null,"prediction":452.01076923076914,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":10,"featureType":null,"prediction":443.46937926330156,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":13,"featureType":"continuous","prediction":null,"threshold":25.325,"categories":null,"feature":0,"overflow":false}
{"index":12,"featureType":null,"prediction":440.73731707317074,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":14,"featureType":null,"prediction":433.86131215469624,"threshold":null,"categories":null,"feature":null,"overflow":false}

Now let's see how our DecisionTree model compares to our LinearRegression model

val predictionsAndLabels = dtModel.bestModel.transform(testSet)
val metrics = new RegressionMetrics(predictionsAndLabels.select("Predicted_PE", "PE").map(r => (r(0).asInstanceOf[Double], r(1).asInstanceOf[Double])).rdd)

val rmse = metrics.rootMeanSquaredError
val explainedVariance = metrics.explainedVariance
val r2 = metrics.r2

println (f"Root Mean Squared Error: $rmse")
println (f"Explained Variance: $explainedVariance")  
println (f"R2: $r2")
Root Mean Squared Error: 5.111944542729953
Explained Variance: 261.4355220034205
R2: 0.908560906504635
predictionsAndLabels: org.apache.spark.sql.DataFrame = [AT: double, V: double ... 5 more fields]
metrics: org.apache.spark.mllib.evaluation.RegressionMetrics = org.apache.spark.mllib.evaluation.RegressionMetrics@684c4c50
rmse: Double = 5.111944542729953
explainedVariance: Double = 261.4355220034205
r2: Double = 0.908560906504635

So our DecisionTree was slightly worse than our LinearRegression model (LR: 4.6 vs DT: 5.2). Maybe we can try an Ensemble method such as Gradient-Boosted Decision Trees to see if we can strengthen our model by using an ensemble of weaker trees with weighting to reduce the error in our model.

*Note since this is a complex model, the cell below can take about *16 minutes* or so to run on a small cluster with a couple nodes with about 6GB RAM, go out and grab a coffee and come back :-).*

This GBTRegressor code will be way faster on a larger cluster of course.

A visual explanation of gradient boosted trees:

Let's see what a boosting algorithm, a type of ensemble method, is all about in more detail.

import org.apache.spark.ml.regression.GBTRegressor

val gbt = new GBTRegressor()
gbt.setLabelCol("PE")
gbt.setPredictionCol("Predicted_PE")
gbt.setFeaturesCol("features")
gbt.setSeed(100088121L)
gbt.setMaxBins(100)
gbt.setMaxIter(120)

val gbtPipeline = new Pipeline()
gbtPipeline.setStages(Array(vectorizer, gbt))
//Let's just resuse our CrossValidator

crossval.setEstimator(gbtPipeline)

val paramGrid = new ParamGridBuilder()
  .addGrid(gbt.maxDepth, Array(2, 3))
  .build()
crossval.setEstimatorParamMaps(paramGrid)

//gbt.explainParams
val gbtModel = crossval.fit(trainingSet)
import org.apache.spark.ml.regression.GBTRegressor
gbt: org.apache.spark.ml.regression.GBTRegressor = gbtr_0a275b363831
gbtPipeline: org.apache.spark.ml.Pipeline = pipeline_8b2722444cff
paramGrid: Array[org.apache.spark.ml.param.ParamMap] =
Array({
	gbtr_0a275b363831-maxDepth: 2
}, {
	gbtr_0a275b363831-maxDepth: 3
})
gbtModel: org.apache.spark.ml.tuning.CrossValidatorModel = CrossValidatorModel: uid=cv_bc136566b6a6, bestModel=pipeline_8b2722444cff, numFolds=3
import org.apache.spark.ml.regression.GBTRegressionModel 

val predictionsAndLabels = gbtModel.bestModel.transform(testSet)
val metrics = new RegressionMetrics(predictionsAndLabels.select("Predicted_PE", "PE").map(r => (r(0).asInstanceOf[Double], r(1).asInstanceOf[Double])).rdd)

val rmse = metrics.rootMeanSquaredError
val explainedVariance = metrics.explainedVariance
val r2 = metrics.r2


println (f"Root Mean Squared Error: $rmse")
println (f"Explained Variance: $explainedVariance")  
println (f"R2: $r2")
Root Mean Squared Error: 3.7034735091301307
Explained Variance: 272.208177448154
R2: 0.9520069744321176
import org.apache.spark.ml.regression.GBTRegressionModel
predictionsAndLabels: org.apache.spark.sql.DataFrame = [AT: double, V: double ... 5 more fields]
metrics: org.apache.spark.mllib.evaluation.RegressionMetrics = org.apache.spark.mllib.evaluation.RegressionMetrics@79d7946a
rmse: Double = 3.7034735091301307
explainedVariance: Double = 272.208177448154
r2: Double = 0.9520069744321176

We can use the toDebugString method to dump out what our trees and weighting look like:

gbtModel.bestModel.asInstanceOf[PipelineModel].stages.last.asInstanceOf[GBTRegressionModel].toDebugString
res116: String =
"GBTRegressionModel: uid=gbtr_0a275b363831, numTrees=120, numFeatures=4
  Tree 0 (weight 1.0):
    If (feature 0 <= 18.595)
     If (feature 0 <= 11.885000000000002)
      If (feature 0 <= 8.575)
       Predict: 483.994943457189
      Else (feature 0 > 8.575)
       Predict: 476.04374262101527
     Else (feature 0 > 11.885000000000002)
      If (feature 0 <= 15.475000000000001)
       Predict: 467.5564649956784
      Else (feature 0 > 15.475000000000001)
       Predict: 459.5010376134889
    Else (feature 0 > 18.595)
     If (feature 1 <= 66.21000000000001)
      If (feature 0 <= 22.055)
       Predict: 452.01076923076914
      Else (feature 0 > 22.055)
       Predict: 443.46937926330156
     Else (feature 1 > 66.21000000000001)
      If (feature 0 <= 25.325)
       Predict: 440.73731707317074
      Else (feature 0 > 25.325)
       Predict: 433.86131215469624
  Tree 1 (weight 0.1):
    If (feature 3 <= 82.55000000000001)
     If (feature 0 <= 26.505000000000003)
      If (feature 3 <= 64.11500000000001)
       Predict: 6.095232469256877
      Else (feature 3 > 64.11500000000001)
       Predict: 1.4337156041793564
     Else (feature 0 > 26.505000000000003)
      If (feature 1 <= 65.55000000000001)
       Predict: -7.6527692217902885
      Else (feature 1 > 65.55000000000001)
       Predict: -0.5844786594493007
    Else (feature 3 > 82.55000000000001)
     If (feature 1 <= 45.754999999999995)
      If (feature 3 <= 93.075)
       Predict: 0.6108402960070604
      Else (feature 3 > 93.075)
       Predict: -3.913147108789527
     Else (feature 1 > 45.754999999999995)
      If (feature 0 <= 18.595)
       Predict: -9.443118256805649
      Else (feature 0 > 18.595)
       Predict: -3.9650066253122347
  Tree 2 (weight 0.1):
    If (feature 1 <= 45.754999999999995)
     If (feature 0 <= 15.475000000000001)
      If (feature 0 <= 14.285)
       Predict: 1.1090321642566017
      Else (feature 0 > 14.285)
       Predict: -3.898383406004269
     Else (feature 0 > 15.475000000000001)
      If (feature 0 <= 18.595)
       Predict: 4.874047316205584
      Else (feature 0 > 18.595)
       Predict: 10.653531335032094
    Else (feature 1 > 45.754999999999995)
     If (feature 0 <= 18.595)
      If (feature 1 <= 58.19)
       Predict: -5.0005796708960615
      Else (feature 1 > 58.19)
       Predict: -13.749053154552547
     Else (feature 0 > 18.595)
      If (feature 2 <= 1009.295)
       Predict: -3.1410617295379555
      Else (feature 2 > 1009.295)
       Predict: 0.8001319329379373
  Tree 3 (weight 0.1):
    If (feature 3 <= 85.52000000000001)
     If (feature 1 <= 55.825)
      If (feature 0 <= 26.505000000000003)
       Predict: 2.695149105254423
      Else (feature 0 > 26.505000000000003)
       Predict: -6.7564705067621675
     Else (feature 1 > 55.825)
      If (feature 1 <= 66.21000000000001)
       Predict: -2.282355645191304
      Else (feature 1 > 66.21000000000001)
       Predict: 0.5508297910243797
    Else (feature 3 > 85.52000000000001)
     If (feature 1 <= 40.629999999999995)
      If (feature 2 <= 1022.8399999999999)
       Predict: 2.236331037122985
      Else (feature 2 > 1022.8399999999999)
       Predict: -7.220151471077029
     Else (feature 1 > 40.629999999999995)
      If (feature 3 <= 89.595)
       Predict: -2.175085332960937
      Else (feature 3 > 89.595)
       Predict: -4.54715329410012
  Tree 4 (weight 0.1):
    If (feature 2 <= 1010.335)
     If (feature 1 <= 43.005)
      If (feature 0 <= 15.475000000000001)
       Predict: -0.004818717215773318
      Else (feature 0 > 15.475000000000001)
       Predict: 5.355639866401019
     Else (feature 1 > 43.005)
      If (feature 1 <= 65.15)
       Predict: -5.132340755716604
      Else (feature 1 > 65.15)
       Predict: -0.7228608840382099
    Else (feature 2 > 1010.335)
     If (feature 3 <= 74.525)
      If (feature 0 <= 29.455)
       Predict: 3.0313483965828176
      Else (feature 0 > 29.455)
       Predict: -2.560863167947768
     Else (feature 3 > 74.525)
      If (feature 1 <= 40.629999999999995)
       Predict: 2.228142113797423
      Else (feature 1 > 40.629999999999995)
       Predict: -1.6052323952407273
  Tree 5 (weight 0.1):
    If (feature 3 <= 81.045)
     If (feature 0 <= 27.585)
      If (feature 3 <= 46.92)
       Predict: 8.005444802948366
      Else (feature 3 > 46.92)
       Predict: 1.301219291279602
     Else (feature 0 > 27.585)
      If (feature 1 <= 65.55000000000001)
       Predict: -6.568175152421089
      Else (feature 1 > 65.55000000000001)
       Predict: -0.8331220915230161
    Else (feature 3 > 81.045)
     If (feature 1 <= 41.519999999999996)
      If (feature 2 <= 1019.835)
       Predict: 1.7054425589091675
      Else (feature 2 > 1019.835)
       Predict: -2.6266728146418195
     Else (feature 1 > 41.519999999999996)
      If (feature 1 <= 41.805)
       Predict: -11.130585327952137
      Else (feature 1 > 41.805)
       Predict: -2.111742422947989
  Tree 6 (weight 0.1):
    If (feature 2 <= 1009.625)
     If (feature 1 <= 43.005)
      If (feature 0 <= 15.475000000000001)
       Predict: -0.4497329015715072
      Else (feature 0 > 15.475000000000001)
       Predict: 3.661440765591046
     Else (feature 1 > 43.005)
      If (feature 1 <= 66.85499999999999)
       Predict: -3.861085082339984
      Else (feature 1 > 66.85499999999999)
       Predict: -0.7492674320362704
    Else (feature 2 > 1009.625)
     If (feature 3 <= 69.32499999999999)
      If (feature 0 <= 29.455)
       Predict: 2.621042446270476
      Else (feature 0 > 29.455)
       Predict: -1.4554021183385886
     Else (feature 3 > 69.32499999999999)
      If (feature 1 <= 58.19)
       Predict: 0.42605173456002876
      Else (feature 1 > 58.19)
       Predict: -1.9554878629891888
  Tree 7 (weight 0.1):
    If (feature 3 <= 86.625)
     If (feature 1 <= 52.795)
      If (feature 0 <= 18.595)
       Predict: 0.4988124937300424
      Else (feature 0 > 18.595)
       Predict: 4.447321094438702
     Else (feature 1 > 52.795)
      If (feature 1 <= 66.21000000000001)
       Predict: -1.721618872277871
      Else (feature 1 > 66.21000000000001)
       Predict: 0.6365209437219329
    Else (feature 3 > 86.625)
     If (feature 0 <= 6.895)
      If (feature 3 <= 87.32499999999999)
       Predict: -10.224737687790185
      Else (feature 3 > 87.32499999999999)
       Predict: 3.712660431036073
     Else (feature 0 > 6.895)
      If (feature 0 <= 8.575)
       Predict: -7.105091794629204
      Else (feature 0 > 8.575)
       Predict: -1.5060749360589718
  Tree 8 (weight 0.1):
    If (feature 2 <= 1008.745)
     If (feature 1 <= 41.665)
      If (feature 0 <= 15.475000000000001)
       Predict: 0.11492519898093705
      Else (feature 0 > 15.475000000000001)
       Predict: 3.532699993937119
     Else (feature 1 > 41.665)
      If (feature 1 <= 66.85499999999999)
       Predict: -3.366654434213031
      Else (feature 1 > 66.85499999999999)
       Predict: -0.9165259817521934
    Else (feature 2 > 1008.745)
     If (feature 3 <= 82.955)
      If (feature 1 <= 51.905)
       Predict: 1.841638760642105
      Else (feature 1 > 51.905)
       Predict: 0.33265178659776373
     Else (feature 3 > 82.955)
      If (feature 3 <= 95.68)
       Predict: -0.4850135884105616
      Else (feature 3 > 95.68)
       Predict: -3.812639024859598
  Tree 9 (weight 0.1):
    If (feature 0 <= 29.455)
     If (feature 3 <= 61.89)
      If (feature 1 <= 71.18)
       Predict: 1.9301726185107941
      Else (feature 1 > 71.18)
       Predict: 8.938327477606107
     Else (feature 3 > 61.89)
      If (feature 0 <= 5.8149999999999995)
       Predict: 4.428862111265314
      Else (feature 0 > 5.8149999999999995)
       Predict: -0.3308347482908286
    Else (feature 0 > 29.455)
     If (feature 1 <= 68.28999999999999)
      If (feature 2 <= 1009.875)
       Predict: -8.941194411728706
      Else (feature 2 > 1009.875)
       Predict: -1.8834474815204216
     Else (feature 1 > 68.28999999999999)
      If (feature 2 <= 1014.405)
       Predict: -0.5760094442636617
      Else (feature 2 > 1014.405)
       Predict: -5.50575933697771
  Tree 10 (weight 0.1):
    If (feature 2 <= 1005.345)
     If (feature 0 <= 27.355)
      If (feature 3 <= 99.3)
       Predict: -0.5544332197918127
      Else (feature 3 > 99.3)
       Predict: -6.049841121821514
     Else (feature 0 > 27.355)
      If (feature 1 <= 70.815)
       Predict: -8.03479585317622
      Else (feature 1 > 70.815)
       Predict: 0.0619269945107018
    Else (feature 2 > 1005.345)
     If (feature 3 <= 72.41499999999999)
      If (feature 0 <= 24.755000000000003)
       Predict: 2.020104454165069
      Else (feature 0 > 24.755000000000003)
       Predict: -0.22964512858748945
     Else (feature 3 > 72.41499999999999)
      If (feature 1 <= 40.7)
       Predict: 1.2987210163143512
      Else (feature 1 > 40.7)
       Predict: -0.8347660227231797
  Tree 11 (weight 0.1):
    If (feature 0 <= 5.0600000000000005)
     If (feature 1 <= 42.3)
      If (feature 1 <= 39.765)
       Predict: 4.261094449524424
      Else (feature 1 > 39.765)
       Predict: 9.140536590115639
     Else (feature 1 > 42.3)
      If (feature 2 <= 1007.835)
       Predict: 0.9746298984436711
      Else (feature 2 > 1007.835)
       Predict: -6.317973546286112
    Else (feature 0 > 5.0600000000000005)
     If (feature 3 <= 95.68)
      If (feature 2 <= 1009.295)
       Predict: -0.8626626541525325
      Else (feature 2 > 1009.295)
       Predict: 0.3906915507169364
     Else (feature 3 > 95.68)
      If (feature 0 <= 11.885000000000002)
       Predict: -6.002679638413293
      Else (feature 0 > 11.885000000000002)
       Predict: -0.7509189525586508
  Tree 12 (weight 0.1):
    If (feature 0 <= 18.595)
     If (feature 1 <= 51.905)
      If (feature 0 <= 13.695)
       Predict: 0.5958576966099496
      Else (feature 0 > 13.695)
       Predict: -1.2694566117501789
     Else (feature 1 > 51.905)
      If (feature 1 <= 58.19)
       Predict: -4.248373100253223
      Else (feature 1 > 58.19)
       Predict: -9.144729000689791
    Else (feature 0 > 18.595)
     If (feature 1 <= 47.64)
      If (feature 2 <= 1012.675)
       Predict: 0.8560563666774771
      Else (feature 2 > 1012.675)
       Predict: 10.801233083620462
     Else (feature 1 > 47.64)
      If (feature 0 <= 20.015)
       Predict: 3.1978561830060213
      Else (feature 0 > 20.015)
       Predict: -0.16716555702980626
  Tree 13 (weight 0.1):
    If (feature 0 <= 28.655)
     If (feature 1 <= 66.21000000000001)
      If (feature 1 <= 58.19)
       Predict: 0.34765099851241454
      Else (feature 1 > 58.19)
       Predict: -1.8189329025195076
     Else (feature 1 > 66.21000000000001)
      If (feature 0 <= 22.525)
       Predict: 6.490484815153365
      Else (feature 0 > 22.525)
       Predict: 0.7933381751314565
    Else (feature 0 > 28.655)
     If (feature 1 <= 68.28999999999999)
      If (feature 2 <= 1005.665)
       Predict: -8.922459399148678
      Else (feature 2 > 1005.665)
       Predict: -2.3989441108132668
     Else (feature 1 > 68.28999999999999)
      If (feature 2 <= 1018.215)
       Predict: -0.3023338438804105
      Else (feature 2 > 1018.215)
       Predict: 14.559949112833806
  Tree 14 (weight 0.1):
    If (feature 0 <= 15.475000000000001)
     If (feature 0 <= 13.695)
      If (feature 0 <= 11.885000000000002)
       Predict: -0.8897676968273979
      Else (feature 0 > 11.885000000000002)
       Predict: 3.5874467728768487
     Else (feature 0 > 13.695)
      If (feature 1 <= 46.345)
       Predict: -3.2690852418064273
      Else (feature 1 > 46.345)
       Predict: -8.844433418899179
    Else (feature 0 > 15.475000000000001)
     If (feature 1 <= 43.175)
      If (feature 1 <= 41.805)
       Predict: 3.298855216614116
      Else (feature 1 > 41.805)
       Predict: 9.150659154207167
     Else (feature 1 > 43.175)
      If (feature 2 <= 1012.495)
       Predict: -0.7109832273625656
      Else (feature 2 > 1012.495)
       Predict: 1.1631179843236674
  Tree 15 (weight 0.1):
    If (feature 3 <= 90.055)
     If (feature 0 <= 30.41)
      If (feature 1 <= 66.21000000000001)
       Predict: -0.01732155577258642
      Else (feature 1 > 66.21000000000001)
       Predict: 1.3432966941310502
     Else (feature 0 > 30.41)
      If (feature 1 <= 69.465)
       Predict: -3.6657811330207344
      Else (feature 1 > 69.465)
       Predict: -0.38803561342243853
    Else (feature 3 > 90.055)
     If (feature 2 <= 1015.725)
      If (feature 1 <= 47.64)
       Predict: 1.5063080039677825
      Else (feature 1 > 47.64)
       Predict: -1.860635777865782
     Else (feature 2 > 1015.725)
      If (feature 1 <= 40.7)
       Predict: 0.21921885078759318
      Else (feature 1 > 40.7)
       Predict: -4.793242614118129
  Tree 16 (weight 0.1):
    If (feature 0 <= 6.895)
     If (feature 3 <= 67.42500000000001)
      If (feature 1 <= 39.620000000000005)
       Predict: -1.8477082180199003
      Else (feature 1 > 39.620000000000005)
       Predict: 16.387935166882745
     Else (feature 3 > 67.42500000000001)
      If (feature 0 <= 5.0600000000000005)
       Predict: 4.152127693563297
      Else (feature 0 > 5.0600000000000005)
       Predict: 0.7556214745509566
    Else (feature 0 > 6.895)
     If (feature 0 <= 8.575)
      If (feature 2 <= 1022.8399999999999)
       Predict: -2.9436476590152036
      Else (feature 2 > 1022.8399999999999)
       Predict: -8.032234733606465
     Else (feature 0 > 8.575)
      If (feature 0 <= 9.325)
       Predict: 5.082738415532321
      Else (feature 0 > 9.325)
       Predict: -0.032287806549855816
  Tree 17 (weight 0.1):
    If (feature 3 <= 61.89)
     If (feature 0 <= 28.655)
      If (feature 0 <= 11.885000000000002)
       Predict: -4.455566502931916
      Else (feature 0 > 11.885000000000002)
       Predict: 1.9027943448616742
     Else (feature 0 > 28.655)
      If (feature 1 <= 66.21000000000001)
       Predict: -3.1810487244675034
      Else (feature 1 > 66.21000000000001)
       Predict: 0.11525363261816625
    Else (feature 3 > 61.89)
     If (feature 1 <= 43.175)
      If (feature 0 <= 18.595)
       Predict: 0.22262511130066664
      Else (feature 0 > 18.595)
       Predict: 10.13639446335034
     Else (feature 1 > 43.175)
      If (feature 0 <= 22.055)
       Predict: -1.4775024201129299
      Else (feature 0 > 22.055)
       Predict: 0.20591189539330298
  Tree 18 (weight 0.1):
    If (feature 2 <= 1005.345)
     If (feature 1 <= 70.815)
      If (feature 0 <= 23.564999999999998)
       Predict: -0.178777362918765
      Else (feature 0 > 23.564999999999998)
       Predict: -4.52113806132068
     Else (feature 1 > 70.815)
      If (feature 3 <= 60.025000000000006)
       Predict: 4.247605743793766
      Else (feature 3 > 60.025000000000006)
       Predict: -0.26865379510738685
    Else (feature 2 > 1005.345)
     If (feature 1 <= 66.21000000000001)
      If (feature 1 <= 55.825)
       Predict: 0.3773109266288433
      Else (feature 1 > 55.825)
       Predict: -1.3659380946007862
     Else (feature 1 > 66.21000000000001)
      If (feature 0 <= 21.335)
       Predict: 8.448170645066464
      Else (feature 0 > 21.335)
       Predict: 0.5048679905700459
  Tree 19 (weight 0.1):
    If (feature 0 <= 18.595)
     If (feature 1 <= 51.905)
      If (feature 0 <= 17.655)
       Predict: -0.003054757854134698
      Else (feature 0 > 17.655)
       Predict: -2.9290357116654935
     Else (feature 1 > 51.905)
      If (feature 1 <= 66.525)
       Predict: -4.061825439604536
      Else (feature 1 > 66.525)
       Predict: -11.67844591879286
    Else (feature 0 > 18.595)
     If (feature 0 <= 23.945)
      If (feature 3 <= 74.525)
       Predict: 3.807909998319029
      Else (feature 3 > 74.525)
       Predict: 0.008459259251505081
     Else (feature 0 > 23.945)
      If (feature 1 <= 74.915)
       Predict: -0.6429811796826012
      Else (feature 1 > 74.915)
       Predict: 2.099670946504916
  Tree 20 (weight 0.1):
    If (feature 0 <= 15.475000000000001)
     If (feature 0 <= 14.285)
      If (feature 0 <= 11.885000000000002)
       Predict: -0.7234702732306101
      Else (feature 0 > 11.885000000000002)
       Predict: 1.589299673192479
     Else (feature 0 > 14.285)
      If (feature 2 <= 1016.495)
       Predict: -2.4381805412578545
      Else (feature 2 > 1016.495)
       Predict: -6.544687605774689
    Else (feature 0 > 15.475000000000001)
     If (feature 1 <= 43.005)
      If (feature 2 <= 1008.405)
       Predict: 0.8119248626873221
      Else (feature 2 > 1008.405)
       Predict: 5.506769369239865
     Else (feature 1 > 43.005)
      If (feature 2 <= 1012.935)
       Predict: -0.5028175384892806
      Else (feature 2 > 1012.935)
       Predict: 1.0290531238165197
  Tree 21 (weight 0.1):
    If (feature 0 <= 6.895)
     If (feature 3 <= 67.42500000000001)
      If (feature 1 <= 39.620000000000005)
       Predict: -0.9752219334588972
      Else (feature 1 > 39.620000000000005)
       Predict: 13.369575512848845
     Else (feature 3 > 67.42500000000001)
      If (feature 1 <= 42.705)
       Predict: 1.850492181024754
      Else (feature 1 > 42.705)
       Predict: -2.033710059657357
    Else (feature 0 > 6.895)
     If (feature 0 <= 8.575)
      If (feature 2 <= 1022.8399999999999)
       Predict: -2.256120115332435
      Else (feature 2 > 1022.8399999999999)
       Predict: -6.380948299395909
     Else (feature 0 > 8.575)
      If (feature 0 <= 9.594999999999999)
       Predict: 3.4448565562285904
      Else (feature 0 > 9.594999999999999)
       Predict: -0.05858832726578875
  Tree 22 (weight 0.1):
    If (feature 0 <= 22.055)
     If (feature 0 <= 21.095)
      If (feature 1 <= 66.21000000000001)
       Predict: -0.17987193554240402
      Else (feature 1 > 66.21000000000001)
       Predict: 6.044335675519052
     Else (feature 0 > 21.095)
      If (feature 1 <= 66.21000000000001)
       Predict: -5.809637597188877
      Else (feature 1 > 66.21000000000001)
       Predict: 2.7761443044302214
    Else (feature 0 > 22.055)
     If (feature 0 <= 23.564999999999998)
      If (feature 1 <= 64.74000000000001)
       Predict: 5.951769778696803
      Else (feature 1 > 64.74000000000001)
       Predict: -0.30197045172071896
     Else (feature 0 > 23.564999999999998)
      If (feature 1 <= 44.519999999999996)
       Predict: -7.283292958317056
      Else (feature 1 > 44.519999999999996)
       Predict: -0.19387573131258415
  Tree 23 (weight 0.1):
    If (feature 3 <= 53.025000000000006)
     If (feature 0 <= 24.945)
      If (feature 0 <= 18.29)
       Predict: 1.0381040338364682
      Else (feature 0 > 18.29)
       Predict: 5.164469183375362
     Else (feature 0 > 24.945)
      If (feature 1 <= 66.21000000000001)
       Predict: -1.0707595335847206
      Else (feature 1 > 66.21000000000001)
       Predict: 0.8108674466901084
    Else (feature 3 > 53.025000000000006)
     If (feature 1 <= 73.725)
      If (feature 1 <= 71.505)
       Predict: -0.0525992725981239
      Else (feature 1 > 71.505)
       Predict: -2.807221561152817
     Else (feature 1 > 73.725)
      If (feature 2 <= 1017.295)
       Predict: 1.037788102485777
      Else (feature 2 > 1017.295)
       Predict: 7.287181806639116
  Tree 24 (weight 0.1):
    If (feature 2 <= 1004.505)
     If (feature 1 <= 70.815)
      If (feature 1 <= 59.144999999999996)
       Predict: -0.3743851611431973
      Else (feature 1 > 59.144999999999996)
       Predict: -4.648812647772385
     Else (feature 1 > 70.815)
      If (feature 0 <= 27.884999999999998)
       Predict: 2.4545579195950995
      Else (feature 0 > 27.884999999999998)
       Predict: -0.32777974793969294
    Else (feature 2 > 1004.505)
     If (feature 0 <= 22.055)
      If (feature 0 <= 20.795)
       Predict: 0.045218490740101897
      Else (feature 0 > 20.795)
       Predict: -3.3620385127109333
     Else (feature 0 > 22.055)
      If (feature 0 <= 22.955)
       Predict: 4.485324626081587
      Else (feature 0 > 22.955)
       Predict: 0.13166549369330485
  Tree 25 (weight 0.1):
    If (feature 0 <= 18.595)
     If (feature 1 <= 58.19)
      If (feature 0 <= 17.655)
       Predict: -0.023636417468335308
      Else (feature 0 > 17.655)
       Predict: -2.607492744918568
     Else (feature 1 > 58.19)
      If (feature 1 <= 66.525)
       Predict: -4.8994505786627665
      Else (feature 1 > 66.525)
       Predict: -10.07085237281708
    Else (feature 0 > 18.595)
     If (feature 0 <= 19.725)
      If (feature 1 <= 66.21000000000001)
       Predict: 2.2716539497960406
      Else (feature 1 > 66.21000000000001)
       Predict: 13.879740983230867
     Else (feature 0 > 19.725)
      If (feature 1 <= 43.005)
       Predict: 5.616411926544602
      Else (feature 1 > 43.005)
       Predict: -0.00532316539213451
  Tree 26 (weight 0.1):
    If (feature 3 <= 93.075)
     If (feature 1 <= 55.825)
      If (feature 0 <= 22.055)
       Predict: 0.15441544139943786
      Else (feature 0 > 22.055)
       Predict: 2.7626508552722306
     Else (feature 1 > 55.825)
      If (feature 1 <= 66.21000000000001)
       Predict: -1.2060290652635515
      Else (feature 1 > 66.21000000000001)
       Predict: 0.4827535356971057
    Else (feature 3 > 93.075)
     If (feature 2 <= 1015.725)
      If (feature 0 <= 7.34)
       Predict: 4.241421869391143
      Else (feature 0 > 7.34)
       Predict: -0.704916847045625
     Else (feature 2 > 1015.725)
      If (feature 0 <= 11.885000000000002)
       Predict: -5.4904249010577795
      Else (feature 0 > 11.885000000000002)
       Predict: 0.0976872424106726
  Tree 27 (weight 0.1):
    If (feature 2 <= 1008.745)
     If (feature 1 <= 41.665)
      If (feature 1 <= 39.765)
       Predict: -1.0511879426704696
      Else (feature 1 > 39.765)
       Predict: 1.894883627758776
     Else (feature 1 > 41.665)
      If (feature 1 <= 41.805)
       Predict: -13.576686832482961
      Else (feature 1 > 41.805)
       Predict: -0.7168167899342832
    Else (feature 2 > 1008.745)
     If (feature 0 <= 15.475000000000001)
      If (feature 0 <= 13.695)
       Predict: 0.303140697564446
      Else (feature 0 > 13.695)
       Predict: -2.8034862119109945
     Else (feature 0 > 15.475000000000001)
      If (feature 1 <= 55.825)
       Predict: 2.0736158373993576
      Else (feature 1 > 55.825)
       Predict: -0.03336709818500243
  Tree 28 (weight 0.1):
    If (feature 2 <= 1001.785)
     If (feature 3 <= 69.86500000000001)
      If (feature 1 <= 69.465)
       Predict: -7.299995136853619
      Else (feature 1 > 69.465)
       Predict: 0.23757420536270835
     Else (feature 3 > 69.86500000000001)
      If (feature 0 <= 7.34)
       Predict: 3.4313360513286284
      Else (feature 0 > 7.34)
       Predict: -1.276734468456009
    Else (feature 2 > 1001.785)
     If (feature 0 <= 11.885000000000002)
      If (feature 0 <= 11.335)
       Predict: 0.04499264982858887
      Else (feature 0 > 11.335)
       Predict: -6.156735713959919
     Else (feature 0 > 11.885000000000002)
      If (feature 0 <= 12.715)
       Predict: 4.4864210547378915
      Else (feature 0 > 12.715)
       Predict: 0.030721690290287165
  Tree 29 (weight 0.1):
    If (feature 1 <= 66.21000000000001)
     If (feature 0 <= 26.505000000000003)
      If (feature 0 <= 22.055)
       Predict: -0.3694472776628706
      Else (feature 0 > 22.055)
       Predict: 1.5208925945902059
     Else (feature 0 > 26.505000000000003)
      If (feature 1 <= 43.510000000000005)
       Predict: -17.99975152056241
      Else (feature 1 > 43.510000000000005)
       Predict: -2.4033598663496183
    Else (feature 1 > 66.21000000000001)
     If (feature 0 <= 22.055)
      If (feature 0 <= 18.595)
       Predict: -7.600012529438
      Else (feature 0 > 18.595)
       Predict: 6.469471961408998
     Else (feature 0 > 22.055)
      If (feature 0 <= 25.325)
       Predict: -2.6540186758683166
      Else (feature 0 > 25.325)
       Predict: 0.9869775581610103
  Tree 30 (weight 0.1):
    If (feature 0 <= 5.0600000000000005)
     If (feature 1 <= 42.3)
      If (feature 3 <= 95.68)
       Predict: 2.6307256050737506
      Else (feature 3 > 95.68)
       Predict: 7.168878406232186
     Else (feature 1 > 42.3)
      If (feature 2 <= 1007.835)
       Predict: -0.1884983669158752
      Else (feature 2 > 1007.835)
       Predict: -5.920088632100639
    Else (feature 0 > 5.0600000000000005)
     If (feature 1 <= 37.815)
      If (feature 0 <= 11.885000000000002)
       Predict: -3.8096010917307517
      Else (feature 0 > 11.885000000000002)
       Predict: 3.5943708074284917
     Else (feature 1 > 37.815)
      If (feature 1 <= 41.519999999999996)
       Predict: 0.6752927073561888
      Else (feature 1 > 41.519999999999996)
       Predict: -0.14342050966250913
  Tree 31 (weight 0.1):
    If (feature 3 <= 99.3)
     If (feature 0 <= 31.155)
      If (feature 3 <= 46.92)
       Predict: 2.011051499336945
      Else (feature 3 > 46.92)
       Predict: 0.012791339921714258
     Else (feature 0 > 31.155)
      If (feature 2 <= 1014.405)
       Predict: -0.916397796921109
      Else (feature 2 > 1014.405)
       Predict: -6.832504867736499
    Else (feature 3 > 99.3)
     If (feature 1 <= 39.765)
      If (feature 1 <= 38.41)
       Predict: -5.505405887296888
      Else (feature 1 > 38.41)
       Predict: -16.748187635942333
     Else (feature 1 > 39.765)
      If (feature 0 <= 16.04)
       Predict: 0.7708563952983728
      Else (feature 0 > 16.04)
       Predict: -3.909609799859729
  Tree 32 (weight 0.1):
    If (feature 1 <= 66.21000000000001)
     If (feature 1 <= 64.74000000000001)
      If (feature 2 <= 1011.515)
       Predict: -1.0002623040885374
      Else (feature 2 > 1011.515)
       Predict: 0.3591184679910596
     Else (feature 1 > 64.74000000000001)
      If (feature 2 <= 1006.775)
       Predict: -13.788703659238209
      Else (feature 2 > 1006.775)
       Predict: -2.4620285364725656
    Else (feature 1 > 66.21000000000001)
     If (feature 1 <= 69.09)
      If (feature 0 <= 22.525)
       Predict: 6.088217885246919
      Else (feature 0 > 22.525)
       Predict: 1.0364537580784474
     Else (feature 1 > 69.09)
      If (feature 0 <= 25.325)
       Predict: -2.7946704533493856
      Else (feature 0 > 25.325)
       Predict: 0.6607665941219878
  Tree 33 (weight 0.1):
    If (feature 2 <= 1028.14)
     If (feature 0 <= 29.455)
      If (feature 1 <= 66.21000000000001)
       Predict: -0.08158010506593574
      Else (feature 1 > 66.21000000000001)
       Predict: 0.8815313937000332
     Else (feature 0 > 29.455)
      If (feature 1 <= 44.519999999999996)
       Predict: -12.581939252812768
      Else (feature 1 > 44.519999999999996)
       Predict: -0.77008278158028
    Else (feature 2 > 1028.14)
     If (feature 0 <= 8.575)
      If (feature 1 <= 39.45)
       Predict: 0.6766771966451415
      Else (feature 1 > 39.45)
       Predict: -8.445008186341592
     Else (feature 0 > 8.575)
      If (feature 0 <= 8.96)
       Predict: 3.777292703648982
      Else (feature 0 > 8.96)
       Predict: -2.398045803854934
  Tree 34 (weight 0.1):
    If (feature 0 <= 6.895)
     If (feature 3 <= 67.42500000000001)
      If (feature 1 <= 39.620000000000005)
       Predict: -0.6804590872791323
      Else (feature 1 > 39.620000000000005)
       Predict: 10.518093452986212
     Else (feature 3 > 67.42500000000001)
      If (feature 1 <= 42.705)
       Predict: 1.3098801739379287
      Else (feature 1 > 42.705)
       Predict: -1.7450883352732074
    Else (feature 0 > 6.895)
     If (feature 0 <= 8.575)
      If (feature 0 <= 7.765)
       Predict: -0.7816329288490581
      Else (feature 0 > 7.765)
       Predict: -3.7319393815256547
     Else (feature 0 > 8.575)
      If (feature 0 <= 9.965)
       Predict: 2.5600814387681337
      Else (feature 0 > 9.965)
       Predict: -0.06944896856946733
  Tree 35 (weight 0.1):
    If (feature 3 <= 61.89)
     If (feature 1 <= 39.34)
      If (feature 0 <= 16.695)
       Predict: -4.078381955056753
      Else (feature 0 > 16.695)
       Predict: -16.616821684050763
     Else (feature 1 > 39.34)
      If (feature 1 <= 40.82)
       Predict: 4.4394084324272045
      Else (feature 1 > 40.82)
       Predict: 0.4663514281701948
    Else (feature 3 > 61.89)
     If (feature 1 <= 58.19)
      If (feature 0 <= 22.055)
       Predict: -0.027831559557693095
      Else (feature 0 > 22.055)
       Predict: 2.492136574233702
     Else (feature 1 > 58.19)
      If (feature 0 <= 18.595)
       Predict: -4.183073089901298
      Else (feature 0 > 18.595)
       Predict: -0.40866909936948326
  Tree 36 (weight 0.1):
    If (feature 2 <= 1004.505)
     If (feature 1 <= 38.754999999999995)
      If (feature 3 <= 77.195)
       Predict: 9.579430817769946
      Else (feature 3 > 77.195)
       Predict: 2.6305173165509195
     Else (feature 1 > 38.754999999999995)
      If (feature 1 <= 70.065)
       Predict: -1.801035005150415
      Else (feature 1 > 70.065)
       Predict: 0.4054557218074593
    Else (feature 2 > 1004.505)
     If (feature 2 <= 1017.475)
      If (feature 1 <= 43.175)
       Predict: 1.09341093192285
      Else (feature 1 > 43.175)
       Predict: -0.03229585395374685
     Else (feature 2 > 1017.475)
      If (feature 2 <= 1019.365)
       Predict: -1.7719467091167656
      Else (feature 2 > 1019.365)
       Predict: 0.2537098831339789
  Tree 37 (weight 0.1):
    If (feature 0 <= 15.475000000000001)
     If (feature 0 <= 13.695)
      If (feature 0 <= 11.885000000000002)
       Predict: -0.5104239863875834
      Else (feature 0 > 11.885000000000002)
       Predict: 2.1202163252308432
     Else (feature 0 > 13.695)
      If (feature 3 <= 78.38499999999999)
       Predict: -3.379040627299855
      Else (feature 3 > 78.38499999999999)
       Predict: -0.9911440360990582
    Else (feature 0 > 15.475000000000001)
     If (feature 0 <= 16.395)
      If (feature 3 <= 67.42500000000001)
       Predict: 0.4887402058080506
      Else (feature 3 > 67.42500000000001)
       Predict: 3.884289185845989
     Else (feature 0 > 16.395)
      If (feature 2 <= 1020.565)
       Predict: -0.02862374251288089
      Else (feature 2 > 1020.565)
       Predict: 3.15734851002617
  Tree 38 (weight 0.1):
    If (feature 3 <= 43.385)
     If (feature 0 <= 24.945)
      If (feature 2 <= 1014.405)
       Predict: 1.603183026814036
      Else (feature 2 > 1014.405)
       Predict: 7.05673098720603
     Else (feature 0 > 24.945)
      If (feature 0 <= 26.295)
       Predict: -5.886157652325024
      Else (feature 0 > 26.295)
       Predict: 0.7387886738447553
    Else (feature 3 > 43.385)
     If (feature 1 <= 73.725)
      If (feature 1 <= 71.505)
       Predict: 0.008754170391068655
      Else (feature 1 > 71.505)
       Predict: -2.0178119354056765
     Else (feature 1 > 73.725)
      If (feature 1 <= 77.42)
       Predict: 1.8396223170900134
      Else (feature 1 > 77.42)
       Predict: -1.5747478023010713
  Tree 39 (weight 0.1):
    If (feature 0 <= 22.055)
     If (feature 0 <= 20.795)
      If (feature 0 <= 18.595)
       Predict: -0.25201916420658693
      Else (feature 0 > 18.595)
       Predict: 1.5718496558845116
     Else (feature 0 > 20.795)
      If (feature 1 <= 66.21000000000001)
       Predict: -3.7201562729508804
      Else (feature 1 > 66.21000000000001)
       Predict: 2.087916157719636
    Else (feature 0 > 22.055)
     If (feature 0 <= 23.564999999999998)
      If (feature 2 <= 1012.015)
       Predict: 0.7371264627237751
      Else (feature 2 > 1012.015)
       Predict: 4.6381746481309065
     Else (feature 0 > 23.564999999999998)
      If (feature 1 <= 44.519999999999996)
       Predict: -5.772062593218147
      Else (feature 1 > 44.519999999999996)
       Predict: -0.12977023255758624
  Tree 40 (weight 0.1):
    If (feature 0 <= 5.0600000000000005)
     If (feature 3 <= 95.68)
      If (feature 2 <= 1011.105)
       Predict: -3.365769010003795
      Else (feature 2 > 1011.105)
       Predict: 2.955050770650336
     Else (feature 3 > 95.68)
      If (feature 2 <= 1008.205)
       Predict: 2.728200788704399
      Else (feature 2 > 1008.205)
       Predict: 6.919382935391042
    Else (feature 0 > 5.0600000000000005)
     If (feature 3 <= 96.61)
      If (feature 1 <= 37.815)
       Predict: -1.3949762323292278
      Else (feature 1 > 37.815)
       Predict: 0.06411431759031856
     Else (feature 3 > 96.61)
      If (feature 0 <= 11.605)
       Predict: -3.491961189446582
      Else (feature 0 > 11.605)
       Predict: -0.16406940197018208
  Tree 41 (weight 0.1):
    If (feature 0 <= 30.41)
     If (feature 1 <= 66.21000000000001)
      If (feature 1 <= 58.85)
       Predict: 0.15540001609212736
      Else (feature 1 > 58.85)
       Predict: -1.1352706510871309
     Else (feature 1 > 66.21000000000001)
      If (feature 0 <= 25.325)
       Predict: -0.6390388689881783
      Else (feature 0 > 25.325)
       Predict: 1.3909471658872326
    Else (feature 0 > 30.41)
     If (feature 2 <= 1014.405)
      If (feature 1 <= 56.894999999999996)
       Predict: -9.841212730443857
      Else (feature 1 > 56.894999999999996)
       Predict: -0.5054201979116707
     Else (feature 2 > 1014.405)
      If (feature 1 <= 74.915)
       Predict: -5.898616989217175
      Else (feature 1 > 74.915)
       Predict: 1.042314191558674
  Tree 42 (weight 0.1):
    If (feature 2 <= 1009.625)
     If (feature 1 <= 43.005)
      If (feature 1 <= 42.025000000000006)
       Predict: -0.05077288158998095
      Else (feature 1 > 42.025000000000006)
       Predict: 3.619244461816007
     Else (feature 1 > 43.005)
      If (feature 0 <= 18.595)
       Predict: -3.5057172058309307
      Else (feature 0 > 18.595)
       Predict: -0.32537979322253646
    Else (feature 2 > 1009.625)
     If (feature 2 <= 1017.475)
      If (feature 1 <= 55.825)
       Predict: 0.8076710222538108
      Else (feature 1 > 55.825)
       Predict: -0.01784249647067053
     Else (feature 2 > 1017.475)
      If (feature 2 <= 1019.365)
       Predict: -1.4312272708033218
      Else (feature 2 > 1019.365)
       Predict: 0.20844195286029432
  Tree 43 (weight 0.1):
    If (feature 0 <= 18.595)
     If (feature 0 <= 17.655)
      If (feature 0 <= 15.475000000000001)
       Predict: -0.2913115404147692
      Else (feature 0 > 15.475000000000001)
       Predict: 1.1145997107947745
     Else (feature 0 > 17.655)
      If (feature 1 <= 37.815)
       Predict: 14.538914074443028
      Else (feature 1 > 37.815)
       Predict: -3.0407663665320683
    Else (feature 0 > 18.595)
     If (feature 2 <= 1020.325)
      If (feature 1 <= 43.175)
       Predict: 3.881117973012625
      Else (feature 1 > 43.175)
       Predict: 0.04538590552170286
     Else (feature 2 > 1020.325)
      If (feature 1 <= 64.74000000000001)
       Predict: 4.662857871344832
      Else (feature 1 > 64.74000000000001)
       Predict: -43.5190245896606
  Tree 44 (weight 0.1):
    If (feature 0 <= 6.895)
     If (feature 3 <= 67.42500000000001)
      If (feature 1 <= 39.620000000000005)
       Predict: -0.7153417257252007
      Else (feature 1 > 39.620000000000005)
       Predict: 8.417772324738223
     Else (feature 3 > 67.42500000000001)
      If (feature 2 <= 1010.985)
       Predict: 2.5111312207852263
      Else (feature 2 > 1010.985)
       Predict: 0.29950092637128345
    Else (feature 0 > 6.895)
     If (feature 0 <= 8.575)
      If (feature 1 <= 40.06)
       Predict: -3.30672576579827
      Else (feature 1 > 40.06)
       Predict: -0.45097750406116727
     Else (feature 0 > 8.575)
      If (feature 0 <= 9.325)
       Predict: 3.226884779601992
      Else (feature 0 > 9.325)
       Predict: -0.041218673012550146
  Tree 45 (weight 0.1):
    If (feature 2 <= 1028.14)
     If (feature 0 <= 10.395)
      If (feature 3 <= 92.22999999999999)
       Predict: 1.0355113706204075
      Else (feature 3 > 92.22999999999999)
       Predict: -1.4603765116034264
     Else (feature 0 > 10.395)
      If (feature 0 <= 11.885000000000002)
       Predict: -2.630098257038007
      Else (feature 0 > 11.885000000000002)
       Predict: 0.09582680902226459
    Else (feature 2 > 1028.14)
     If (feature 0 <= 8.575)
      If (feature 1 <= 39.45)
       Predict: 1.107359449029309
      Else (feature 1 > 39.45)
       Predict: -6.096185488604492
     Else (feature 0 > 8.575)
      If (feature 3 <= 70.57499999999999)
       Predict: -3.516006231223605
      Else (feature 3 > 70.57499999999999)
       Predict: -0.26144006873351155
  Tree 46 (weight 0.1):
    If (feature 0 <= 27.884999999999998)
     If (feature 1 <= 66.21000000000001)
      If (feature 0 <= 25.145)
       Predict: 0.06412914679730906
      Else (feature 0 > 25.145)
       Predict: -1.554041618425865
     Else (feature 1 > 66.21000000000001)
      If (feature 0 <= 25.325)
       Predict: -0.4748636523867588
      Else (feature 0 > 25.325)
       Predict: 2.4595627925276826
    Else (feature 0 > 27.884999999999998)
     If (feature 3 <= 61.89)
      If (feature 1 <= 71.895)
       Predict: -0.4429995884239883
      Else (feature 1 > 71.895)
       Predict: 1.4321627506429122
     Else (feature 3 > 61.89)
      If (feature 1 <= 71.505)
       Predict: -0.2617373838209719
      Else (feature 1 > 71.505)
       Predict: -2.637373068367584
  Tree 47 (weight 0.1):
    If (feature 3 <= 61.89)
     If (feature 1 <= 39.34)
      If (feature 0 <= 16.695)
       Predict: -2.855821258258964
      Else (feature 0 > 16.695)
       Predict: -13.80709248590955
     Else (feature 1 > 39.34)
      If (feature 1 <= 74.915)
       Predict: 0.35443616318343385
      Else (feature 1 > 74.915)
       Predict: 2.9400682899293233
    Else (feature 3 > 61.89)
     If (feature 1 <= 71.505)
      If (feature 1 <= 66.85499999999999)
       Predict: -0.142107366817925
      Else (feature 1 > 66.85499999999999)
       Predict: 1.0352328327059535
     Else (feature 1 > 71.505)
      If (feature 1 <= 73.00999999999999)
       Predict: -2.947898208728739
      Else (feature 1 > 73.00999999999999)
       Predict: -0.0830706492691125
  Tree 48 (weight 0.1):
    If (feature 2 <= 1004.505)
     If (feature 1 <= 38.754999999999995)
      If (feature 3 <= 86.625)
       Predict: 4.921331281961159
      Else (feature 3 > 86.625)
       Predict: -5.961237317667383
     Else (feature 1 > 38.754999999999995)
      If (feature 1 <= 39.765)
       Predict: -4.436072018762161
      Else (feature 1 > 39.765)
       Predict: -0.7283906418193187
    Else (feature 2 > 1004.505)
     If (feature 0 <= 22.055)
      If (feature 0 <= 20.795)
       Predict: 0.044899959208437666
      Else (feature 0 > 20.795)
       Predict: -2.2295677836603995
     Else (feature 0 > 22.055)
      If (feature 0 <= 23.564999999999998)
       Predict: 2.3559950404053414
      Else (feature 0 > 23.564999999999998)
       Predict: -0.06950420285239005
  Tree 49 (weight 0.1):
    If (feature 1 <= 41.435)
     If (feature 0 <= 11.885000000000002)
      If (feature 0 <= 11.335)
       Predict: -0.02697483446966382
      Else (feature 0 > 11.335)
       Predict: -3.7031660865730367
     Else (feature 0 > 11.885000000000002)
      If (feature 0 <= 13.265)
       Predict: 4.209724879257512
      Else (feature 0 > 13.265)
       Predict: 0.41602586770224464
    Else (feature 1 > 41.435)
     If (feature 1 <= 41.805)
      If (feature 3 <= 89.595)
       Predict: -1.6099299736449546
      Else (feature 3 > 89.595)
       Predict: -9.419799062932288
     Else (feature 1 > 41.805)
      If (feature 1 <= 43.175)
       Predict: 1.5951066240527068
      Else (feature 1 > 43.175)
       Predict: -0.11481901338423915
  Tree 50 (weight 0.1):
    If (feature 1 <= 38.41)
     If (feature 0 <= 11.885000000000002)
      If (feature 2 <= 1016.665)
       Predict: -5.344526613859499
      Else (feature 2 > 1016.665)
       Predict: 0.058134490545794976
     Else (feature 0 > 11.885000000000002)
      If (feature 0 <= 16.985)
       Predict: 1.537246393097642
      Else (feature 0 > 16.985)
       Predict: 9.920778277565365
    Else (feature 1 > 38.41)
     If (feature 0 <= 13.485)
      If (feature 1 <= 51.045)
       Predict: 0.6675749827847329
      Else (feature 1 > 51.045)
       Predict: -5.737026170963195
     Else (feature 0 > 13.485)
      If (feature 0 <= 15.475000000000001)
       Predict: -1.7210713764803844
      Else (feature 0 > 15.475000000000001)
       Predict: 0.09027853735147576
  Tree 51 (weight 0.1):
    If (feature 0 <= 31.155)
     If (feature 3 <= 48.230000000000004)
      If (feature 2 <= 1020.325)
       Predict: 0.9307527734280435
      Else (feature 2 > 1020.325)
       Predict: 9.070547343579028
     Else (feature 3 > 48.230000000000004)
      If (feature 1 <= 73.725)
       Predict: -0.06359121142988887
      Else (feature 1 > 73.725)
       Predict: 1.049949579330099
    Else (feature 0 > 31.155)
     If (feature 1 <= 63.08)
      If (feature 1 <= 44.519999999999996)
       Predict: -6.355864033256125
      Else (feature 1 > 44.519999999999996)
       Predict: 13.6760008529786
     Else (feature 1 > 63.08)
      If (feature 1 <= 68.28999999999999)
       Predict: -3.953494984806905
      Else (feature 1 > 68.28999999999999)
       Predict: -0.6145841300086397
  Tree 52 (weight 0.1):
    If (feature 2 <= 1012.495)
     If (feature 1 <= 41.435)
      If (feature 1 <= 39.975)
       Predict: -0.4047468839922722
      Else (feature 1 > 39.975)
       Predict: 2.509624688414308
     Else (feature 1 > 41.435)
      If (feature 1 <= 41.805)
       Predict: -6.811044477667833
      Else (feature 1 > 41.805)
       Predict: -0.26889174065489546
    Else (feature 2 > 1012.495)
     If (feature 3 <= 92.22999999999999)
      If (feature 1 <= 58.19)
       Predict: 0.7048711166950787
      Else (feature 1 > 58.19)
       Predict: -0.5475390646726656
     Else (feature 3 > 92.22999999999999)
      If (feature 1 <= 41.805)
       Predict: -3.7013459723577355
      Else (feature 1 > 41.805)
       Predict: 0.7237930378019226
  Tree 53 (weight 0.1):
    If (feature 0 <= 18.595)
     If (feature 0 <= 17.335)
      If (feature 3 <= 74.08500000000001)
       Predict: -0.8631764946312587
      Else (feature 3 > 74.08500000000001)
       Predict: 0.2803856631344212
     Else (feature 0 > 17.335)
      If (feature 1 <= 42.705)
       Predict: 0.9335711174385192
      Else (feature 1 > 42.705)
       Predict: -2.950020164379197
    Else (feature 0 > 18.595)
     If (feature 2 <= 1013.395)
      If (feature 1 <= 66.85499999999999)
       Predict: -0.7231135633124072
      Else (feature 1 > 66.85499999999999)
       Predict: 0.41724670068145925
     Else (feature 2 > 1013.395)
      If (feature 1 <= 58.19)
       Predict: 4.568024116358373
      Else (feature 1 > 58.19)
       Predict: -0.36270787813043714
  Tree 54 (weight 0.1):
    If (feature 2 <= 1001.785)
     If (feature 3 <= 63.575)
      If (feature 3 <= 60.025000000000006)
       Predict: -1.7427137986580719
      Else (feature 3 > 60.025000000000006)
       Predict: -7.776342039375448
     Else (feature 3 > 63.575)
      If (feature 0 <= 27.119999999999997)
       Predict: 0.026174663094801796
      Else (feature 0 > 27.119999999999997)
       Predict: -2.343138620856655
    Else (feature 2 > 1001.785)
     If (feature 0 <= 22.055)
      If (feature 1 <= 66.21000000000001)
       Predict: -0.27236570115397085
      Else (feature 1 > 66.21000000000001)
       Predict: 3.164590339421908
     Else (feature 0 > 22.055)
      If (feature 0 <= 22.725)
       Predict: 2.9597120242025485
      Else (feature 0 > 22.725)
       Predict: 0.054881549113388446
  Tree 55 (weight 0.1):
    If (feature 2 <= 1028.14)
     If (feature 1 <= 45.754999999999995)
      If (feature 0 <= 26.715)
       Predict: 0.2599176823406179
      Else (feature 0 > 26.715)
       Predict: -5.549910372715466
     Else (feature 1 > 45.754999999999995)
      If (feature 0 <= 15.475000000000001)
       Predict: -2.867925531108855
      Else (feature 0 > 15.475000000000001)
       Predict: -0.0236838100703647
    Else (feature 2 > 1028.14)
     If (feature 0 <= 8.575)
      If (feature 1 <= 39.45)
       Predict: 0.7777761733424086
      Else (feature 1 > 39.45)
       Predict: -5.202001886405932
     Else (feature 0 > 8.575)
      If (feature 3 <= 68.945)
       Predict: -3.641368616696809
      Else (feature 3 > 68.945)
       Predict: -0.6008141057791702
  Tree 56 (weight 0.1):
    If (feature 3 <= 61.89)
     If (feature 0 <= 18.29)
      If (feature 2 <= 1019.025)
       Predict: -2.1632736300070996
      Else (feature 2 > 1019.025)
       Predict: 1.2430029950309498
     Else (feature 0 > 18.29)
      If (feature 1 <= 44.91)
       Predict: 3.2134324628571003
      Else (feature 1 > 44.91)
       Predict: 0.2988556025240279
    Else (feature 3 > 61.89)
     If (feature 1 <= 71.505)
      If (feature 1 <= 66.85499999999999)
       Predict: -0.09866504525517336
      Else (feature 1 > 66.85499999999999)
       Predict: 0.7271499788275563
     Else (feature 1 > 71.505)
      If (feature 1 <= 73.00999999999999)
       Predict: -2.395971400707892
      Else (feature 1 > 73.00999999999999)
       Predict: -0.16608323426526406
  Tree 57 (weight 0.1):
    If (feature 2 <= 1017.645)
     If (feature 2 <= 1014.615)
      If (feature 1 <= 43.175)
       Predict: 1.0389282601473917
      Else (feature 1 > 43.175)
       Predict: -0.3646675630154698
     Else (feature 2 > 1014.615)
      If (feature 1 <= 43.510000000000005)
       Predict: -0.6889797697082773
      Else (feature 1 > 43.510000000000005)
       Predict: 1.5908362409321974
    Else (feature 2 > 1017.645)
     If (feature 2 <= 1019.025)
      If (feature 1 <= 71.18)
       Predict: -1.6569133708803008
      Else (feature 1 > 71.18)
       Predict: 4.314967971455512
     Else (feature 2 > 1019.025)
      If (feature 3 <= 89.595)
       Predict: 0.43765066032139976
      Else (feature 3 > 89.595)
       Predict: -1.7344432288008194
  Tree 58 (weight 0.1):
    If (feature 2 <= 1004.505)
     If (feature 1 <= 70.815)
      If (feature 1 <= 59.834999999999994)
       Predict: -0.170418541124326
      Else (feature 1 > 59.834999999999994)
       Predict: -2.895038840312831
     Else (feature 1 > 70.815)
      If (feature 2 <= 1000.505)
       Predict: -1.3832637115340176
      Else (feature 2 > 1000.505)
       Predict: 1.2249185299155396
    Else (feature 2 > 1004.505)
     If (feature 0 <= 22.055)
      If (feature 1 <= 66.21000000000001)
       Predict: -0.2418541439735617
      Else (feature 1 > 66.21000000000001)
       Predict: 3.0110894160107886
     Else (feature 0 > 22.055)
      If (feature 0 <= 23.945)
       Predict: 1.4999960684883906
      Else (feature 0 > 23.945)
       Predict: -0.042407486119460915
  Tree 59 (weight 0.1):
    If (feature 1 <= 77.42)
     If (feature 1 <= 74.915)
      If (feature 1 <= 71.505)
       Predict: 0.03983464447255206
      Else (feature 1 > 71.505)
       Predict: -0.7683021525819648
     Else (feature 1 > 74.915)
      If (feature 3 <= 72.82)
       Predict: 2.774179202497669
      Else (feature 3 > 72.82)
       Predict: -0.32979787820368633
    Else (feature 1 > 77.42)
     If (feature 0 <= 21.595)
      If (feature 0 <= 21.335)
       Predict: -13.565760771414489
      Else (feature 0 > 21.335)
       Predict: -13.954507897669714
     Else (feature 0 > 21.595)
      If (feature 0 <= 22.955)
       Predict: 10.853700477067264
      Else (feature 0 > 22.955)
       Predict: -1.4643467280880287
  Tree 60 (weight 0.1):
    If (feature 0 <= 10.395)
     If (feature 1 <= 40.629999999999995)
      If (feature 3 <= 75.545)
       Predict: -2.3127871072788375
      Else (feature 3 > 75.545)
       Predict: 0.3992391857664209
     Else (feature 1 > 40.629999999999995)
      If (feature 3 <= 89.595)
       Predict: 2.9152362525803523
      Else (feature 3 > 89.595)
       Predict: -1.4086879927580456
    Else (feature 0 > 10.395)
     If (feature 0 <= 11.885000000000002)
      If (feature 2 <= 1025.2150000000001)
       Predict: -2.2352340341897547
      Else (feature 2 > 1025.2150000000001)
       Predict: 5.952010328542228
     Else (feature 0 > 11.885000000000002)
      If (feature 0 <= 12.415)
       Predict: 3.4957190546300447
      Else (feature 0 > 12.415)
       Predict: -0.03992973893781255
  Tree 61 (weight 0.1):
    If (feature 1 <= 40.82)
     If (feature 1 <= 40.224999999999994)
      If (feature 3 <= 75.545)
       Predict: -1.2944988036912455
      Else (feature 3 > 75.545)
       Predict: 0.44866615475817667
     Else (feature 1 > 40.224999999999994)
      If (feature 2 <= 1025.2150000000001)
       Predict: 0.7826360308981203
      Else (feature 2 > 1025.2150000000001)
       Predict: 9.875672812487991
    Else (feature 1 > 40.82)
     If (feature 2 <= 1025.2150000000001)
      If (feature 0 <= 10.945)
       Predict: 1.1628421208118285
      Else (feature 0 > 10.945)
       Predict: -0.12551627485602937
     Else (feature 2 > 1025.2150000000001)
      If (feature 1 <= 41.15)
       Predict: -7.782369290305258
      Else (feature 1 > 41.15)
       Predict: -1.200273276366743
  Tree 62 (weight 0.1):
    If (feature 0 <= 22.055)
     If (feature 0 <= 21.335)
      If (feature 1 <= 66.21000000000001)
       Predict: -0.09621281022933233
      Else (feature 1 > 66.21000000000001)
       Predict: 2.680549669942832
     Else (feature 0 > 21.335)
      If (feature 1 <= 63.864999999999995)
       Predict: -3.207766197974041
      Else (feature 1 > 63.864999999999995)
       Predict: -0.14162445042909583
    Else (feature 0 > 22.055)
     If (feature 0 <= 22.725)
      If (feature 2 <= 1011.515)
       Predict: 0.5064350504779975
      Else (feature 2 > 1011.515)
       Predict: 3.659612527058891
     Else (feature 0 > 22.725)
      If (feature 3 <= 75.545)
       Predict: 0.2595183211083464
      Else (feature 3 > 75.545)
       Predict: -0.6564588168227348
  Tree 63 (weight 0.1):
    If (feature 2 <= 1017.645)
     If (feature 1 <= 44.67)
      If (feature 1 <= 44.13)
       Predict: 0.3869693354075677
      Else (feature 1 > 44.13)
       Predict: 4.723132901950317
     Else (f...

Conclusion

Wow! So our best model is in fact our Gradient Boosted Decision tree model which uses an ensemble of 120 Trees with a depth of 3 to construct a better model than the single decision tree.

Step 8: Deployment will be done later

Now that we have a predictive model it is time to deploy the model into an operational environment.

In our example, let's say we have a series of sensors attached to the power plant and a monitoring station.

The monitoring station will need close to real-time information about how much power that their station will generate so they can relay that to the utility.

For this we need to create a Spark Streaming utility that we can use for this purpose. For this you need to be introduced to basic concepts in Spark Streaming first. See http://spark.apache.org/docs/latest/streaming-programming-guide.html if you can't wait!

After deployment you will be able to use the best predictions from gradient boosed regression trees to feed a real-time dashboard or feed the utility with information on how much power the peaker plant will deliver give current conditions.

Persisting Statistical Machine Learning Models

See https://databricks.com/blog/2016/05/31/apache-spark-2-0-preview-machine-learning-model-persistence.html

Let's save our best model so we can load it without having to rerun the validation and training again.

gbtModel
res117: org.apache.spark.ml.tuning.CrossValidatorModel = CrossValidatorModel: uid=cv_bc136566b6a6, bestModel=pipeline_8b2722444cff, numFolds=3
gbtModel.bestModel.asInstanceOf[PipelineModel]
        .write.overwrite().save("/databricks/driver/MyTrainedBestPipelineModel")

When it is time to deploy the trained model to serve predicitons, we can simply reload this model and proceed as shown later.

This is one of the Deploymnet Patterns for Serving a Model's Prediction.

See: https://learning.oreilly.com/library/view/spark-the-definitive/9781491912201/ch24.html#deployment-patterns

Datasource References:

  • Pinar Tüfekci, Prediction of full load electrical power output of a base load operated combined cycle power plant using machine learning methods, International Journal of Electrical Power & Energy Systems, Volume 60, September 2014, Pages 126-140, ISSN 0142-0615, Web Link
  • Heysem Kaya, Pinar Tüfekci , Sadik Fikret Gürgen: Local and Global Learning Methods for Predicting Power of a Combined Gas & Steam Turbine, Proceedings of the International Conference on Emerging Trends in Computer and Electronics Engineering ICETCEE 2012, pp. 13-18 (Mar. 2012, Dubai) Web Link

ScaDaMaLe Course site and book

Activity Recognition from Accelerometer

  1. ETL Using SparkSQL Windows

  1. Prediction using Random Forest

This work is a simpler databricksification of Amira Lakhal's more complex framework for activity recognition:

Amira's video

See Section below on 0. Download and Load Data first.

  • Once data is loaded come back here (if you have not downloaded and loaded data into the distributed file system under your hood).
val data = sc.textFile("/datasets/sds/ActivityRecognition/dataTraining.csv") // assumes data is loaded
data: org.apache.spark.rdd.RDD[String] = /datasets/sds/ActivityRecognition/dataTraining.csv MapPartitionsRDD[256] at textFile at command-2971213210275754:1
data.take(5).foreach(println)
"user_id","activity","timeStampAsLong","x","y","z"
"user_001","Jumping",1446047227606,"4.33079","-12.72175","-3.18118"
"user_001","Jumping",1446047227671,"0.575403","-0.727487","2.95007"
"user_001","Jumping",1446047227735,"-1.60885","3.52607","-0.1922"
"user_001","Jumping",1446047227799,"0.690364","-0.037722","1.72382"
val dataDF = sqlContext.read    
    .format("com.databricks.spark.csv") // use spark.csv package
    .option("header", "true") // Use first line of all files as header
    .option("inferSchema", "true") // Automatically infer data types
    .option("delimiter", ",") // Specify the delimiter as ','
    .load("/datasets/sds/ActivityRecognition/dataTraining.csv")
dataDF: org.apache.spark.sql.DataFrame = [user_id: string, activity: string ... 4 more fields]
val dataDFnew = spark.read.format("csv") 
  .option("inferSchema", "true") 
  .option("header", "true") 
  .option("sep", ",") 
  .load("/datasets/sds/ActivityRecognition/dataTraining.csv")
dataDFnew: org.apache.spark.sql.DataFrame = [user_id: string, activity: string ... 4 more fields]
dataDFnew.printSchema()
root
 |-- user_id: string (nullable = true)
 |-- activity: string (nullable = true)
 |-- timeStampAsLong: long (nullable = true)
 |-- x: double (nullable = true)
 |-- y: double (nullable = true)
 |-- z: double (nullable = true)
display(dataDF) // zp.show(dataDF)
user_id activity timeStampAsLong x y z
user_001 Jumping 1.446047227606e12 4.33079 -12.72175 -3.18118
user_001 Jumping 1.446047227671e12 0.575403 -0.727487 2.95007
user_001 Jumping 1.446047227735e12 -1.60885 3.52607 -0.1922
user_001 Jumping 1.446047227799e12 0.690364 -3.7722e-2 1.72382
user_001 Jumping 1.446047227865e12 3.44943 -1.68549 2.29862
user_001 Jumping 1.44604722793e12 1.87829 -1.91542 0.880768
user_001 Jumping 1.446047227995e12 1.57173 -5.86241 -3.75599
user_001 Jumping 1.446047228059e12 3.41111 -17.93331 0.535886
user_001 Jumping 1.446047228123e12 3.18118 -19.58108 5.74745
user_001 Jumping 1.446047228189e12 7.85626 -19.2362 0.804128
user_001 Jumping 1.446047228253e12 1.26517 -8.85139 2.18366
user_001 Jumping 1.446047228318e12 7.7239e-2 1.15021 1.53221
user_001 Jumping 1.446047228383e12 0.230521 2.0699 -1.41845
user_001 Jumping 1.446047228447e12 0.652044 -0.497565 1.76214
user_001 Jumping 1.446047228512e12 1.53341 -0.305964 1.41725
user_001 Jumping 1.446047228578e12 -1.07237 -1.95374 0.191003
user_001 Jumping 1.446047228642e12 2.75966 -13.75639 0.191003
user_001 Jumping 1.446047228707e12 7.43474 -19.58108 2.95007
user_001 Jumping 1.446047228771e12 5.63368 -19.58108 5.59417
user_001 Jumping 1.446047228836e12 5.02056 -11.72542 -1.38013
user_001 Jumping 1.4460472289e12 -2.10702 0.575403 1.07237
user_001 Jumping 1.446047228966e12 -1.30229 2.2615 -1.26517
user_001 Jumping 1.44604722903e12 1.68669 -0.957409 1.57053
user_001 Jumping 1.446047229095e12 2.60638 -0.229323 2.14534
user_001 Jumping 1.446047229159e12 1.30349 -0.152682 0.497565
user_001 Jumping 1.446047229224e12 1.64837 -8.12331 1.60885
user_001 Jumping 1.44604722929e12 0.15388 -18.46979 -1.03525
user_001 Jumping 1.446047229354e12 4.98224 -19.58108 0.995729
user_001 Jumping 1.446047229419e12 5.17384 -19.2362 0.612526
user_001 Jumping 1.446047229483e12 2.03158 -9.11964 1.34061
user_001 Jumping 1.446047229549e12 -1.95374 -1.03405 0.574206
user_001 Jumping 1.446047229612e12 0.1922 1.30349 -1.03525
user_001 Jumping 1.446047229678e12 1.64837 -0.727487 -0.307161
user_001 Jumping 1.446047229743e12 2.56806 -1.03405 0.267643
user_001 Jumping 1.446047229806e12 1.41845 -0.305964 0.727487
user_001 Jumping 1.446047229872e12 1.03525 -6.82042 0.957409
user_001 Jumping 1.446047229936e12 3.94759 -19.31284 -1.22685
user_001 Jumping 1.446047230001e12 6.13185 -19.58108 2.72014
user_001 Jumping 1.446047230066e12 7.89458 -16.9753 0.229323
user_001 Jumping 1.446047230131e12 2.6447 -3.75479 0.114362
user_001 Jumping 1.446047230195e12 -2.41358 1.91661 -5.99e-4
user_001 Jumping 1.44604723026e12 -1.95374 -0.114362 -0.268841
user_001 Jumping 1.446047230325e12 -0.229323 -1.95374 2.75846
user_001 Jumping 1.44604723039e12 2.68302 0.268841 0.535886
user_001 Jumping 1.446047230455e12 1.15021 -1.41725 0.880768
user_001 Jumping 1.446047230519e12 2.98958 -11.53382 -0.920286
user_001 Jumping 1.446047230584e12 8.00954 -19.58108 -0.1922
user_001 Jumping 1.446047230649e12 7.31978 -19.58108 2.52854
user_001 Jumping 1.446047230713e12 5.44208 -13.56479 -0.498763
user_001 Jumping 1.446047230779e12 0.728685 -0.420925 1.68549
user_001 Jumping 1.446047230842e12 1.18853 1.41845 -2.22318
user_001 Jumping 1.446047230907e12 0.15388 -1.80046 2.03038
user_001 Jumping 1.446047230972e12 -3.7722e-2 1.07357 -0.958607
user_001 Jumping 1.446047231038e12 0.230521 0.728685 -0.690364
user_001 Jumping 1.446047231102e12 0.805325 -1.14901 1.53221
user_001 Jumping 1.446047231167e12 5.17384 -9.15796 -2.91294
user_001 Jumping 1.446047231231e12 8.00954 -19.54276 1.49389
user_001 Jumping 1.446047231296e12 11.61165 -19.58108 4.25296
user_001 Jumping 1.446047231361e12 7.89458 -18.35483 3.71647
user_001 Jumping 1.446047231426e12 0.537083 -3.21831 0.420925
user_001 Jumping 1.44604723149e12 -1.91542 4.10087 -2.6447
user_001 Jumping 1.446047231555e12 -0.919089 -0.382604 0.114362
user_001 Jumping 1.44604723162e12 0.613724 -0.842448 1.57053
user_001 Jumping 1.446047231684e12 1.38013 -0.459245 0.305964
user_001 Jumping 1.446047231749e12 2.29982 -1.49389 -1.26517
user_001 Jumping 1.446047231814e12 4.94392 -10.95901 -0.498763
user_001 Jumping 1.446047231878e12 3.75599 -19.27452 -1.76333
user_001 Jumping 1.446047231944e12 7.70298 -19.58108 -2.95126
user_001 Jumping 1.446047232008e12 6.55337 -17.51178 -1.91661
user_001 Jumping 1.446047232073e12 2.10822 -2.03038 -0.268841
user_001 Jumping 1.446047232138e12 -1.68549 3.67935 -0.881966
user_001 Jumping 1.446047232203e12 0.15388 -0.114362 7.6042e-2
user_001 Jumping 1.446047232267e12 2.79798 -1.95374 0.689167
user_001 Jumping 1.446047232332e12 1.45677 -0.957409 0.420925
user_001 Jumping 1.446047232397e12 1.18853 -2.95007 0.650847
user_001 Jumping 1.446047232462e12 3.44943 -13.87135 -3.71767
user_001 Jumping 1.446047232526e12 3.79431 -19.58108 -0.345482
user_001 Jumping 1.446047232591e12 6.09353 -19.58108 2.87342
user_001 Jumping 1.446047232655e12 4.48408 -14.3312 -0.498763
user_001 Jumping 1.44604723272e12 -3.7722e-2 -1.68549 2.6435
user_001 Jumping 1.446047232785e12 0.613724 2.68302 -2.37646
user_001 Jumping 1.44604723285e12 0.996927 -0.497565 0.497565
user_001 Jumping 1.446047232915e12 0.15388 -0.689167 1.34061
user_001 Jumping 1.446047232979e12 1.07357 1.07357 -2.60638
user_001 Jumping 1.446047233044e12 2.37646 -3.29495 -1.45677
user_001 Jumping 1.446047233109e12 2.22318 -16.09393 1.37893
user_001 Jumping 1.446047233173e12 6.82161 -19.58108 3.7722e-2
user_001 Jumping 1.446047233238e12 8.39275 -19.54276 1.22565
user_001 Jumping 1.446047233303e12 1.22685 -9.50284 -0.307161
user_001 Jumping 1.446047233368e12 1.83997 -0.152682 1.41725
user_001 Jumping 1.446047233432e12 -0.765807 0.996927 -1.91661
user_001 Jumping 1.446047233497e12 0.728685 -0.612526 0.152682
user_001 Jumping 1.446047233562e12 0.996927 -0.305964 0.995729
user_001 Jumping 1.446047233626e12 1.22685 -0.305964 3.7722e-2
user_001 Jumping 1.446047233692e12 1.91661 -2.95007 -0.345482
user_001 Jumping 1.446047233755e12 4.75232 -14.63776 -3.67935
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user_001 Jumping 1.446047234986e12 5.36544 -4.09967 -0.537083
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user_001 Jumping 1.446047235115e12 6.93658 -19.58108 -2.75966
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user_001 Jumping 1.446047235439e12 1.03525 -1.80046 1.64717
user_001 Jumping 1.446047235504e12 1.95493 -0.689167 1.49389
user_001 Jumping 1.446047235569e12 1.26517 0.383802 -0.307161
user_001 Jumping 1.446047235633e12 1.18853 -2.72014 1.41725
user_001 Jumping 1.446047235698e12 5.71033 -16.51545 -2.03158
user_001 Jumping 1.446047235763e12 6.55337 -19.58108 0.995729
user_001 Jumping 1.446047235828e12 10.577 -19.4278 -1.57173
user_001 Jumping 1.446047235892e12 2.79798 -9.88604 -0.843646
user_001 Jumping 1.446047235957e12 0.652044 -3.7722e-2 1.14901
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user_001 Jumping 1.446047236086e12 0.15388 -0.305964 0.995729
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user_001 Jumping 1.446047236346e12 7.05154 -17.97163 -1.61005
user_001 Jumping 1.44604723641e12 9.46572 -19.58108 2.10702
user_001 Jumping 1.446047236475e12 7.58802 -18.54643 3.10335
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user_001 Jumping 1.446047237122e12 5.97857 -17.78002 0.344284
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user_001 Jumping 1.446047237317e12 -1.64717 -0.650847 1.41725
user_001 Jumping 1.446047237381e12 1.30349 -0.152682 1.45557
user_001 Jumping 1.446047237446e12 2.79798 5.99e-4 -0.460442
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user_001 Jumping 1.44604723764e12 4.98224 -19.27452 1.57053
user_001 Jumping 1.446047237705e12 12.22478 -19.58108 2.0687
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user_001 Jumping 1.446047238352e12 10.53868 -19.58108 0.919089
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user_001 Jumping 1.446047238611e12 0.537083 -0.497565 1.76214
user_001 Jumping 1.446047238676e12 1.95493 0.230521 1.60885
user_001 Jumping 1.446047238741e12 0.920286 0.537083 -0.422122
user_001 Jumping 1.446047238806e12 5.99e-4 -0.650847 0.497565
user_001 Jumping 1.44604723887e12 1.64837 -1.99206 -1.72501
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user_001 Jumping 1.446047239e12 10.50036 -19.58108 1.91542
user_001 Jumping 1.446047239064e12 8.16283 -19.58108 1.95374
user_001 Jumping 1.446047239129e12 3.56439 -9.4262 -1.22685
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user_001 Jumping 1.446047239453e12 1.26517 -0.305964 -5.99e-4
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user_001 Jumping 1.446047239647e12 9.58068 -19.58108 1.53221
user_001 Jumping 1.446047239712e12 8.04786 -19.2362 2.0687
user_001 Jumping 1.446047239777e12 1.80165 -6.01569 -0.422122
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user_001 Jumping 1.446047240036e12 0.843646 1.11189 -0.537083
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user_001 Jumping 1.446047240295e12 7.39642 -19.58108 1.11069
user_001 Jumping 1.44604724036e12 10.23212 -19.58108 0.459245
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user_001 Jumping 1.446047240618e12 0.268841 -1.91542 3.06503
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user_001 Jumping 1.446047240813e12 0.920286 -0.535886 -1.91661
user_001 Jumping 1.446047240878e12 4.40743 -11.61046 0.459245
user_001 Jumping 1.446047240941e12 6.78329 -19.58108 4.82776
user_001 Jumping 1.446047241007e12 9.35075 -19.58108 5.74745
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user_001 Jumping 1.446047242107e12 2.03158 -0.382604 7.6042e-2
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user_002 Standing 1.446309443582e12 -2.14534 -9.2346 -3.8919e-2
user_002 Standing 1.446309443647e12 -2.29862 -9.19628 -5.99e-4
user_002 Standing 1.446309443711e12 -2.29862 -9.19628 3.7722e-2
user_002 Standing 1.446309443776e12 -2.18366 -9.2346 -3.8919e-2
user_002 Standing 1.446309443841e12 -2.10702 -9.19628 3.7722e-2
user_002 Standing 1.446309443906e12 -2.10702 -9.15796 3.7722e-2
user_002 Standing 1.446309443971e12 -2.29862 -9.15796 0.114362
user_002 Standing 1.446309444036e12 -2.03038 -9.27292 -5.99e-4
user_002 Standing 1.4463094441e12 -2.10702 -9.19628 7.6042e-2
user_002 Standing 1.446309444165e12 -2.14534 -9.2346 3.7722e-2
user_002 Standing 1.44630944423e12 -2.22198 -9.19628 7.6042e-2
user_002 Standing 1.446309444295e12 -2.33694 -9.19628 0.191003
user_002 Standing 1.446309444359e12 -2.10702 -9.31124 0.114362
user_002 Standing 1.446309444424e12 -2.0687 -9.2346 -5.99e-4
user_002 Standing 1.446309444489e12 -2.03038 -9.2346 0.114362
user_002 Standing 1.446309444554e12 -2.41358 -9.00468 0.191003
user_002 Standing 1.446309444618e12 -2.37526 -9.19628 0.267643
user_002 Standing 1.446309444683e12 -2.14534 -9.2346 7.6042e-2
user_002 Standing 1.446309444748e12 -2.0687 -9.27292 7.6042e-2
user_002 Standing 1.446309444812e12 -2.33694 -9.2346 0.229323
user_002 Standing 1.446309444877e12 -2.2603 -9.19628 0.229323
user_002 Standing 1.446309444941e12 -2.18366 -9.2346 0.152682
user_002 Standing 1.446309445007e12 -2.22198 -9.2346 0.229323
user_002 Standing 1.446309445072e12 -2.22198 -9.15796 0.191003
user_002 Standing 1.446309445137e12 -2.10702 -9.27292 0.191003
user_002 Standing 1.446309445202e12 -2.10702 -9.31124 0.191003
user_002 Standing 1.446309445265e12 -1.91542 -9.34956 0.191003
user_002 Standing 1.446309445331e12 -1.83878 -9.2346 0.191003
user_002 Standing 1.446309445395e12 -1.91542 -9.08132 0.305964
user_002 Standing 1.446309445459e12 -1.95374 -9.19628 0.152682
user_002 Standing 1.446309445525e12 -1.83878 -9.34956 7.6042e-2
user_002 Standing 1.44630944559e12 -1.80046 -9.31124 7.6042e-2
user_002 Standing 1.446309445654e12 -1.68549 -9.38788 0.267643
user_002 Standing 1.446309445719e12 -1.80046 -9.19628 0.267643
user_002 Standing 1.446309445784e12 -1.76214 -9.34956 -5.99e-4
user_002 Standing 1.446309445849e12 -1.91542 -9.2346 0.152682
user_002 Standing 1.446309445913e12 -1.80046 -9.27292 0.152682
user_002 Standing 1.446309445978e12 -1.76214 -9.27292 0.152682
user_002 Standing 1.446309446043e12 -1.83878 -9.31124 0.152682
user_002 Standing 1.446309446108e12 -1.83878 -9.2346 0.152682
user_002 Standing 1.446309446173e12 -1.8771 -9.27292 0.229323
user_002 Standing 1.446309446237e12 -1.8771 -9.27292 0.229323
user_002 Standing 1.446309446302e12 -1.8771 -9.2346 0.191003
user_002 Standing 1.446309446367e12 -1.8771 -9.31124 0.191003
user_002 Standing 1.446309446432e12 -1.8771 -9.31124 0.152682
user_002 Standing 1.446309446496e12 -1.91542 -9.27292 0.191003
user_002 Standing 1.446309446561e12 -1.8771 -9.2346 0.229323
user_002 Standing 1.446309446625e12 -1.83878 -9.27292 0.152682
user_002 Standing 1.446309446691e12 -1.91542 -9.27292 7.6042e-2
user_002 Standing 1.446309446755e12 -1.8771 -9.31124 0.267643
user_002 Standing 1.44630944682e12 -1.80046 -9.27292 0.267643
user_002 Standing 1.446309446884e12 -1.80046 -9.27292 0.152682
user_002 Standing 1.44630944695e12 -1.72382 -9.31124 7.6042e-2
user_002 Standing 1.446309447014e12 -1.68549 -9.31124 7.6042e-2
user_002 Standing 1.446309447079e12 -1.83878 -9.31124 0.267643
user_002 Standing 1.446309447144e12 -1.8771 -9.27292 0.152682
user_002 Standing 1.446309447209e12 -1.76214 -9.19628 0.152682
user_002 Standing 1.446309447273e12 -1.72382 -9.27292 0.152682
user_002 Standing 1.446309447338e12 -1.83878 -9.27292 0.267643
user_002 Standing 1.446309447403e12 -1.8771 -9.31124 0.229323
user_002 Standing 1.446309447467e12 -1.83878 -9.31124 7.6042e-2
user_002 Standing 1.446309447532e12 -1.68549 -9.34956 7.6042e-2
user_002 Standing 1.446309447597e12 -1.68549 -9.34956 0.152682
user_002 Standing 1.446309447662e12 -1.72382 -9.2346 0.191003
user_002 Standing 1.446309447726e12 -1.8771 -9.31124 0.152682
user_002 Standing 1.446309447791e12 -1.80046 -9.31124 0.152682
user_002 Standing 1.446309447855e12 -1.64717 -9.31124 0.114362
user_002 Standing 1.446309447921e12 -1.60885 -9.27292 0.114362
user_002 Standing 1.446309447986e12 -1.68549 -9.27292 0.229323
user_002 Standing 1.44630944805e12 -1.76214 -9.34956 0.191003
user_002 Standing 1.446309448115e12 -1.72382 -9.34956 0.191003
user_002 Standing 1.44630944818e12 -1.72382 -9.27292 0.267643
user_002 Standing 1.446309448245e12 -1.64717 -9.31124 0.229323
user_002 Standing 1.446309448309e12 -1.64717 -9.27292 0.152682
user_002 Standing 1.446309448374e12 -1.72382 -9.31124 0.229323
user_002 Standing 1.446309448439e12 -1.72382 -9.34956 0.267643
user_002 Standing 1.446309448504e12 -1.72382 -9.2346 0.191003
user_002 Standing 1.446309448569e12 -1.64717 -9.31124 0.152682
user_002 Standing 1.446309448633e12 -1.72382 -9.27292 0.191003
user_002 Standing 1.446309448698e12 -1.68549 -9.27292 0.191003
user_002 Standing 1.446309448763e12 -1.68549 -9.27292 0.152682
user_002 Standing 1.446309448827e12 -1.64717 -9.31124 0.267643
user_002 Standing 1.446309448892e12 -1.64717 -9.34956 0.229323
user_002 Standing 1.446309448957e12 -1.60885 -9.31124 7.6042e-2
user_002 Standing 1.446309449022e12 -1.60885 -9.34956 0.152682
user_002 Standing 1.446309449087e12 -1.68549 -9.31124 0.229323
user_002 Standing 1.446309449151e12 -1.76214 -9.27292 0.229323
user_002 Standing 1.446309449216e12 -1.68549 -9.31124 0.152682
user_002 Standing 1.446309449281e12 -1.68549 -9.31124 7.6042e-2
user_002 Standing 1.446309449346e12 -1.72382 -9.2346 0.191003
user_002 Standing 1.44630944941e12 -1.64717 -9.34956 0.267643
user_002 Standing 1.446309449475e12 -1.76214 -9.27292 0.191003
user_002 Standing 1.44630944954e12 -1.64717 -9.31124 -5.99e-4
user_002 Standing 1.446309449605e12 -1.64717 -9.31124 0.229323
user_002 Standing 1.446309449669e12 -1.68549 -9.27292 0.229323
user_002 Standing 1.446309449734e12 -1.68549 -9.31124 7.6042e-2
user_002 Standing 1.446309449799e12 -1.76214 -9.31124 0.114362
user_002 Standing 1.446309449864e12 -1.76214 -9.27292 0.229323
user_002 Standing 1.446309449928e12 -1.72382 -9.31124 0.229323
user_002 Standing 1.446309449993e12 -1.72382 -9.34956 0.152682
user_002 Standing 1.446309450057e12 -1.72382 -9.34956 0.114362
user_002 Standing 1.446309450123e12 -1.72382 -9.31124 0.267643
user_002 Standing 1.446309450188e12 -1.68549 -9.34956 0.152682
user_002 Standing 1.446309450252e12 -1.83878 -9.31124 0.114362
user_002 Standing 1.446309450317e12 -1.68549 -9.34956 0.191003
user_002 Standing 1.446309450381e12 -1.72382 -9.31124 0.191003
user_002 Standing 1.446309450446e12 -1.68549 -9.34956 3.7722e-2
user_002 Standing 1.446309450511e12 -1.68549 -9.27292 0.229323
user_002 Standing 1.446309450576e12 -1.76214 -9.31124 0.229323
user_002 Standing 1.446309450641e12 -1.72382 -9.31124 0.152682
user_002 Standing 1.446309450705e12 -1.64717 -9.27292 0.152682
user_002 Standing 1.44630945077e12 -1.72382 -9.34956 0.114362
user_002 Standing 1.446309450835e12 -1.83878 -9.2346 0.191003
dataDF.count()
res5: Long = 13679
dataDF.select($"user_id").distinct().show()
+--------+
| user_id|
+--------+
|user_002|
|user_006|
|user_005|
|user_001|
|user_007|
|user_003|
|user_004|
+--------+
dataDF.select($"activity").distinct().show()
+--------+
|activity|
+--------+
| Sitting|
| Walking|
| Jumping|
|Standing|
| Jogging|
+--------+
val sDF = dataDF.sample(false,0.105, 12345L)
sDF.count
sDF: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [user_id: string, activity: string ... 4 more fields]
res8: Long = 1427
sDF.show(5)
+--------+--------+---------------+--------+---------+--------+
| user_id|activity|timeStampAsLong|       x|        y|       z|
+--------+--------+---------------+--------+---------+--------+
|user_001| Jumping|  1446047227671|0.575403|-0.727487| 2.95007|
|user_001| Jumping|  1446047228253| 1.26517| -8.85139| 2.18366|
|user_001| Jumping|  1446047228836| 5.02056|-11.72542|-1.38013|
|user_001| Jumping|  1446047229354| 4.98224|-19.58108|0.995729|
|user_001| Jumping|  1446047229419| 5.17384| -19.2362|0.612526|
+--------+--------+---------------+--------+---------+--------+
only showing top 5 rows
sDF.show(5)
+--------+--------+---------------+--------+---------+--------+
| user_id|activity|timeStampAsLong|       x|        y|       z|
+--------+--------+---------------+--------+---------+--------+
|user_001| Jumping|  1446047227671|0.575403|-0.727487| 2.95007|
|user_001| Jumping|  1446047228253| 1.26517| -8.85139| 2.18366|
|user_001| Jumping|  1446047228836| 5.02056|-11.72542|-1.38013|
|user_001| Jumping|  1446047229354| 4.98224|-19.58108|0.995729|
|user_001| Jumping|  1446047229419| 5.17384| -19.2362|0.612526|
+--------+--------+---------------+--------+---------+--------+
only showing top 5 rows
display(dataDF.sample(false,0.1))
user_id activity timeStampAsLong x y z
user_001 Jumping 1.446047227995e12 1.57173 -5.86241 -3.75599
user_001 Jumping 1.446047228578e12 -1.07237 -1.95374 0.191003
user_001 Jumping 1.446047228771e12 5.63368 -19.58108 5.59417
user_001 Jumping 1.446047229419e12 5.17384 -19.2362 0.612526
user_001 Jumping 1.446047230131e12 2.6447 -3.75479 0.114362
user_001 Jumping 1.446047230713e12 5.44208 -13.56479 -0.498763
user_001 Jumping 1.446047230972e12 -3.7722e-2 1.07357 -0.958607
user_001 Jumping 1.446047231102e12 0.805325 -1.14901 1.53221
user_001 Jumping 1.446047231878e12 3.75599 -19.27452 -1.76333
user_001 Jumping 1.446047232655e12 4.48408 -14.3312 -0.498763
user_001 Jumping 1.446047233044e12 2.37646 -3.29495 -1.45677
user_001 Jumping 1.446047236863e12 -0.650847 -0.305964 -1.15021
user_001 Jumping 1.446047238223e12 2.60638 -3.40991 -0.422122
user_001 Jumping 1.446047239e12 10.50036 -19.58108 1.91542
user_001 Jumping 1.446047239647e12 9.58068 -19.58108 1.53221
user_001 Jumping 1.446047240166e12 3.29615 -3.98471 -0.422122
user_001 Jumping 1.446047241007e12 9.35075 -19.58108 5.74745
user_001 Jumping 1.446047241072e12 5.71033 -15.74905 -1.15021
user_001 Jumping 1.446047241395e12 -0.382604 -0.842448 0.382604
user_001 Jumping 1.446047241459e12 -0.765807 -1.41725 7.6042e-2
user_001 Jumping 1.446047241977e12 0.15388 -0.919089 2.18366
user_001 Jumping 1.446047242042e12 -0.995729 0.460442 0.305964
user_001 Jumping 1.446047242495e12 0.11556 0.613724 -1.30349
user_001 Jumping 1.446047242819e12 5.32712 -13.21991 -1.34181
user_001 Jumping 1.446047243401e12 0.537083 -1.26397 0.535886
user_001 Jumping 1.446047243855e12 -0.535886 -0.957409 1.18733
user_001 Jumping 1.44604724392e12 3.60271 -0.114362 0.574206
user_003 Jumping 1.446047779006e12 -0.574206 -9.00468 -1.76333
user_003 Jumping 1.446047779071e12 -3.14167 -4.36792 -1.68669
user_003 Jumping 1.446047779783e12 -1.72382 -13.98632 -4.10087
user_003 Jumping 1.446047781013e12 -3.06503 -6.70546 -1.76333
user_003 Jumping 1.446047781272e12 -0.689167 -5.55585 -2.37646
user_003 Jumping 1.446047782373e12 -1.64717 -5.90073 -2.33814
user_003 Jumping 1.446047782632e12 -3.40991 -19.54276 -5.71033
user_003 Jumping 1.44604778328e12 -2.41358 -5.59417 -0.613724
user_003 Jumping 1.446047784834e12 -2.4519 1.22685 -1.41845
user_003 Jumping 1.446047784964e12 -0.842448 0.422122 -0.996927
user_003 Jumping 1.446047785741e12 -5.67081 -19.58108 -6.59169
user_003 Jumping 1.446047786388e12 -1.41725 -8.85139 -1.38013
user_003 Jumping 1.446047787489e12 -1.26397 -9.34956 -3.06622
user_003 Jumping 1.446047787553e12 -3.44823 -6.47553 -2.75966
user_003 Jumping 1.446047787812e12 -2.22198 -5.24928 -2.0699
user_003 Jumping 1.446047788136e12 -3.14167 2.72134 -0.575403
user_003 Jumping 1.44604778859e12 -1.83878 -9.77108 -3.25783
user_003 Jumping 1.446047788654e12 -3.14167 -6.55217 -2.6447
user_003 Jumping 1.446047789366e12 -0.689167 0.230521 -0.728685
user_003 Jumping 1.44604778956e12 -3.29495 -18.96796 -5.05888
user_003 Jumping 1.446047789625e12 -2.22198 -12.0703 -3.98591
user_003 Jumping 1.446047790337e12 1.15021 -0.919089 1.64717
user_003 Jumping 1.446047794093e12 -2.10702 -5.93905 -2.14654
user_003 Jumping 1.446047794416e12 5.99e-4 -10.76741 -2.33814
user_002 Standing 1.446309439406e12 -2.8351 -9.11964 -0.958607
user_002 Standing 1.446309439414e12 -2.8351 -8.96635 -1.15021
user_002 Standing 1.446309439609e12 -2.6435 -9.04299 -0.996927
user_002 Standing 1.446309439649e12 -2.60518 -9.11964 -0.843646
user_002 Standing 1.446309439803e12 -2.87342 -8.85139 -0.843646
user_002 Standing 1.446309439892e12 -3.02671 -8.85139 -0.613724
user_002 Standing 1.446309440054e12 -3.10335 -9.11964 -1.07357
user_002 Standing 1.446309440337e12 -3.14167 -8.85139 -0.613724
user_002 Standing 1.446309440394e12 -3.21831 -9.00468 -0.460442
user_002 Standing 1.446309440474e12 -3.02671 -8.96635 -0.767005
user_002 Standing 1.44630944058e12 -3.06503 -8.88971 -0.498763
user_002 Standing 1.446309440587e12 -3.10335 -8.85139 -0.575403
user_002 Standing 1.446309440645e12 -3.10335 -9.08132 -0.383802
user_002 Standing 1.44630944066e12 -3.17999 -8.85139 -0.422122
user_002 Standing 1.446309440717e12 -3.06503 -8.88971 -0.383802
user_002 Standing 1.446309440822e12 -3.06503 -8.96635 -0.460442
user_002 Standing 1.446309440936e12 -3.25663 -8.92803 -0.460442
user_002 Standing 1.44630944096e12 -3.33327 -8.85139 -0.498763
user_002 Standing 1.446309441041e12 -2.91174 -8.96635 -0.383802
user_002 Standing 1.446309441154e12 -3.17999 -9.00468 -0.537083
user_002 Standing 1.44630944117e12 -3.25663 -9.11964 -0.460442
user_002 Standing 1.446309441349e12 -3.44823 -9.00468 -0.383802
user_002 Standing 1.446309441357e12 -3.25663 -8.92803 -0.230521
user_002 Standing 1.446309441373e12 -3.44823 -8.96635 -0.268841
user_002 Standing 1.446309441381e12 -3.40991 -8.85139 -0.345482
user_002 Standing 1.446309441437e12 -3.17999 -9.00468 -0.383802
user_002 Standing 1.446309441462e12 -3.44823 -8.85139 -0.383802
user_002 Standing 1.446309441639e12 -3.21831 -8.77475 -0.422122
user_002 Standing 1.446309441655e12 -3.06503 -8.96635 -0.383802
user_002 Standing 1.446309441696e12 -3.21831 -8.96635 -0.307161
user_002 Standing 1.446309441793e12 -3.17999 -9.2346 -0.307161
user_002 Standing 1.446309442012e12 -3.25663 -9.11964 -5.99e-4
user_002 Standing 1.446309442068e12 -2.95007 -9.08132 -5.99e-4
user_002 Standing 1.446309442287e12 -2.87342 -9.08132 -0.268841
user_002 Standing 1.446309443258e12 -2.18366 -9.15796 3.7722e-2
user_002 Standing 1.446309443582e12 -2.14534 -9.2346 -3.8919e-2
user_002 Standing 1.446309443841e12 -2.10702 -9.19628 3.7722e-2
user_002 Standing 1.446309445072e12 -2.22198 -9.15796 0.191003
user_002 Standing 1.44630944559e12 -1.80046 -9.31124 7.6042e-2
user_002 Standing 1.446309446755e12 -1.8771 -9.31124 0.267643
user_002 Standing 1.446309447403e12 -1.8771 -9.31124 0.229323
user_002 Standing 1.446309447726e12 -1.8771 -9.31124 0.152682
user_002 Standing 1.44630944805e12 -1.76214 -9.34956 0.191003
user_002 Standing 1.446309448698e12 -1.68549 -9.27292 0.191003
user_002 Standing 1.446309449216e12 -1.68549 -9.31124 0.152682
user_002 Standing 1.446309449928e12 -1.72382 -9.31124 0.229323
user_002 Standing 1.446309450446e12 -1.68549 -9.34956 3.7722e-2
user_002 Standing 1.446309451806e12 -1.68549 -9.27292 0.191003
user_002 Standing 1.446309452907e12 -1.72382 -9.27292 0.229323
user_002 Standing 1.446309453101e12 -1.76214 -9.31124 0.229323
user_002 Standing 1.446309454591e12 -1.72382 -9.31124 0.152682
user_002 Standing 1.44630945485e12 -1.80046 -9.31124 0.114362
user_002 Standing 1.446309455045e12 -1.68549 -9.27292 0.152682
user_002 Standing 1.446309456081e12 -1.72382 -9.31124 0.229323
user_005 Standing 1.446046600265e12 0.268841 -9.46452 0.305964
user_005 Standing 1.446046601237e12 0.307161 -9.4262 0.650847
user_005 Standing 1.446046602725e12 0.345482 -9.4262 0.459245
user_005 Standing 1.44604660402e12 0.307161 -9.34956 0.459245
user_005 Standing 1.446046605509e12 0.345482 -9.46452 0.459245
user_005 Standing 1.446046606026e12 0.345482 -9.38788 0.459245
user_005 Standing 1.446046606867e12 0.268841 -9.38788 0.459245
user_005 Standing 1.446046607386e12 0.307161 -9.4262 0.420925
user_005 Standing 1.44604660758e12 0.345482 -9.4262 0.382604
user_005 Standing 1.446046607903e12 0.383802 -9.38788 0.459245
user_005 Standing 1.44604660868e12 0.307161 -9.46452 0.420925
user_005 Standing 1.446046608939e12 0.307161 -9.46452 0.420925
user_005 Standing 1.446046610557e12 0.345482 -9.4262 0.382604
user_005 Standing 1.446046610816e12 0.307161 -9.34956 0.344284
user_005 Standing 1.446046610881e12 0.268841 -9.4262 0.382604
user_005 Standing 1.446046611982e12 0.307161 -9.46452 0.382604
user_005 Standing 1.44604661237e12 0.307161 -9.38788 0.382604
user_005 Standing 1.446046614442e12 0.460442 -9.38788 0.344284
user_005 Standing 1.446046615218e12 0.230521 -9.4262 0.229323
user_005 Standing 1.446046615607e12 0.307161 -9.54116 0.191003
user_002 Sitting 1.44603456478e12 -0.765807 -0.114362 9.4262
user_002 Sitting 1.44603456491e12 -0.804128 -0.191003 9.4262
user_002 Sitting 1.446034565169e12 -0.842448 -0.152682 9.4262
user_002 Sitting 1.446034566723e12 -0.727487 -0.305964 9.4262
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user_005 Jumping 1.446046639435e12 -0.305964 -2.03038 1.8771
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user_005 Jumping 1.446046645004e12 7.7239e-2 -14.17792 4.36792
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user_001 Walking 1.446047181967e12 1.80165 -6.47553 -5.99e-4
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user_002 Jumping 1.446035042732e12 -0.650847 -0.152682 1.14901
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user_002 Jumping 1.446035044933e12 -2.18366 -4.25296 0.229323
user_002 Jumping 1.446035045516e12 0.460442 -2.2603 0.229323
user_002 Jumping 1.446035046292e12 -0.152682 -1.34061 -7.7239e-2
user_002 Jumping 1.446035046745e12 0.575403 1.30349 -1.87829
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user_003 Sitting 1.446047527172e12 0.498763 -0.612526 9.46452
user_003 Sitting 1.446047527754e12 0.498763 -0.689167 9.4262
user_003 Sitting 1.446047527949e12 0.422122 -0.689167 9.4262
user_003 Sitting 1.446047528466e12 0.460442 -0.689167 9.38788
user_003 Sitting 1.44604752879e12 0.460442 -0.727487 9.4262
user_003 Sitting 1.446047529632e12 0.498763 -0.727487 9.4262
user_003 Sitting 1.446047529672e12 0.383802 -0.765807 9.34956
user_003 Sitting 1.446047530142e12 0.575403 -0.765807 9.46452
user_003 Sitting 1.44604753015e12 0.268841 -0.574206 9.38788
user_003 Sitting 1.446047530231e12 0.460442 -0.612526 9.54116
user_003 Sitting 1.446047530287e12 0.268841 -0.459245 9.38788
user_003 Sitting 1.446047530304e12 0.383802 -0.535886 9.54116
user_003 Sitting 1.446047530481e12 0.383802 -0.727487 9.38788
user_003 Sitting 1.446047530498e12 0.537083 -0.804128 9.38788
user_003 Sitting 1.446047530659e12 0.383802 -0.727487 9.54116
user_003 Sitting 1.446047530806e12 0.498763 -0.842448 9.38788
user_003 Sitting 1.44604753083e12 0.498763 -0.612526 9.4262
user_003 Sitting 1.446047530871e12 0.575403 -0.650847 9.46452
user_003 Sitting 1.446047530927e12 0.460442 -0.727487 9.50284
user_003 Sitting 1.446047530991e12 0.460442 -0.765807 9.46452
user_003 Sitting 1.446047531048e12 0.498763 -0.842448 9.34956
user_003 Sitting 1.446047531072e12 0.537083 -0.842448 9.50284
user_003 Sitting 1.446047531161e12 0.383802 -0.612526 9.4262
user_003 Sitting 1.446047531169e12 0.537083 -0.689167 9.50284
user_003 Sitting 1.446047531275e12 0.307161 -0.804128 9.4262
user_003 Sitting 1.446047531291e12 0.383802 -0.727487 9.34956
user_003 Sitting 1.446047531364e12 0.498763 -0.804128 9.50284
user_003 Sitting 1.446047531526e12 0.307161 -0.574206 9.46452
user_003 Sitting 1.446047531566e12 0.652044 -0.612526 9.50284
user_003 Sitting 1.446047531598e12 0.498763 -0.689167 9.46452
user_003 Sitting 1.446047531809e12 0.498763 -0.689167 9.4262
user_003 Sitting 1.446047531817e12 0.268841 -0.804128 9.27292
user_003 Sitting 1.446047531833e12 0.537083 -0.880768 9.38788
user_003 Sitting 1.446047531841e12 0.537083 -0.842448 9.4262
user_003 Sitting 1.446047531857e12 0.422122 -0.727487 9.6178
user_003 Sitting 1.446047531897e12 0.498763 -0.650847 9.4262
user_003 Sitting 1.446047532003e12 0.575403 -0.574206 9.46452
user_003 Sitting 1.446047532051e12 0.613724 -0.650847 9.38788
user_003 Sitting 1.446047532099e12 0.383802 -0.612526 9.50284
user_003 Sitting 1.446047532165e12 0.422122 -0.574206 9.54116
user_003 Sitting 1.446047532214e12 0.537083 -0.612526 9.54116
user_003 Sitting 1.446047532391e12 0.460442 -0.535886 9.4262
user_003 Sitting 1.44604753278e12 0.460442 -0.535886 9.34956
user_003 Sitting 1.446047533832e12 0.498763 -0.650847 9.46452
user_003 Sitting 1.446047534285e12 0.498763 -0.689167 9.46452
user_003 Sitting 1.446047534738e12 0.460442 -0.650847 9.46452
user_003 Sitting 1.446047534803e12 0.422122 -0.612526 9.46452
user_003 Sitting 1.446047535645e12 0.422122 -0.689167 9.38788
user_003 Sitting 1.446047536357e12 0.498763 -0.612526 9.4262
user_003 Sitting 1.446047537005e12 0.498763 -0.650847 9.46452
user_003 Sitting 1.446047537393e12 0.460442 -0.727487 9.46452
user_003 Sitting 1.446047537522e12 0.460442 -0.650847 9.46452
user_003 Sitting 1.446047537963e12 2.91294 -4.06135 -17.7429
user_003 Sitting 1.446047537979e12 0.537083 -0.574206 9.31124
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user_003 Sitting 1.4460475384e12 0.498763 -0.765807 9.34956
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user_003 Sitting 1.44604753857e12 0.498763 -0.689167 9.46452
user_003 Sitting 1.446047538586e12 0.345482 -0.689167 9.4262
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user_003 Sitting 1.446047538861e12 0.422122 -0.689167 9.46452
user_003 Sitting 1.446047538934e12 0.498763 -0.727487 9.46452
user_003 Sitting 1.446047539015e12 0.690364 -0.727487 9.54116
user_003 Sitting 1.446047539136e12 0.422122 -0.765807 9.38788
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user_003 Sitting 1.446047539711e12 0.422122 -0.727487 9.50284
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user_003 Sitting 1.446047539897e12 0.498763 -0.689167 9.46452
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user_003 Sitting 1.446047540107e12 0.460442 -0.650847 9.34956
user_003 Sitting 1.446047540131e12 0.652044 -0.727487 9.50284
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user_003 Sitting 1.446047540464e12 0.498763 -0.535886 9.31124
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user_004 Walking 1.446046380972e12 -3.44823 -16.51545 -2.98958
user_004 Walking 1.446046380996e12 -6.39889 -18.04827 4.5212
user_004 Walking 1.446046381028e12 -3.44823 -2.75846 -4.25415
user_004 Walking 1.446046381068e12 -3.40991 -2.60518 3.44823
user_004 Walking 1.446046381109e12 -2.6435 -10.26924 2.10702
user_004 Walking 1.446046381166e12 4.63736 -9.92436 -3.29615
user_004 Walking 1.446046381246e12 -3.52487 -6.24561 1.8771
user_004 Walking 1.446046381255e12 -3.02671 -6.82042 1.57053
user_004 Walking 1.446046381344e12 -0.995729 -9.31124 0.919089
user_004 Walking 1.446046381482e12 0.805325 -12.37686 -3.0279
user_004 Walking 1.446046381602e12 -9.27292 -16.51545 -0.460442
user_004 Walking 1.446046381708e12 3.41111 -8.62147 -2.49142
user_004 Walking 1.446046381789e12 -1.03405 -5.51753 1.18733
user_004 Walking 1.446046381838e12 -3.52487 -2.33694 -0.15388
user_004 Walking 1.446046381935e12 2.2615 -8.88971 -5.25048
user_004 Walking 1.446046382072e12 -1.26397 -6.13065 -6.63001
user_004 Walking 1.446046382081e12 -2.60518 -8.23827 -4.02423
user_004 Walking 1.44604638221e12 -4.09967 -3.40991 5.096
user_004 Walking 1.44604638234e12 -4.63616 -4.5212 3.10335
user_004 Walking 1.446046382372e12 -4.02303 -6.74378 1.49389
user_004 Walking 1.44604638251e12 -0.305964 -10.07764 -0.383802
user_004 Walking 1.446046382591e12 1.41845 -11.38053 -1.18853
user_004 Walking 1.44604638268e12 2.33814 -11.72542 1.30229
user_004 Walking 1.446046382703e12 2.98958 -13.52647 1.14901
user_004 Walking 1.44604638272e12 0.268841 -16.17057 -5.99e-4
user_004 Walking 1.446046382736e12 -4.21464 -15.40417 -2.18486
user_004 Walking 1.446046382858e12 2.22318 -7.89339 -2.14654
user_004 Walking 1.446046382939e12 -1.45557 -5.90073 0.880768
user_004 Walking 1.446046382947e12 -1.95374 -5.55585 0.880768
user_004 Walking 1.446046383084e12 1.22685 -8.42987 -8.08618
user_004 Walking 1.446046383109e12 3.25783 -15.05928 -6.89825
user_004 Walking 1.446046383157e12 -0.344284 -11.61046 -6.82161
user_004 Walking 1.44604638323e12 -2.52854 -16.66874 -1.53341
user_004 Jumping 1.446046441725e12 0.767005 1.30349 1.03405
user_004 Jumping 1.446046441855e12 19.50564 -19.58108 -6.28513
user_004 Jumping 1.446046442243e12 0.575403 1.15021 -0.690364
user_004 Jumping 1.446046442502e12 6.89825 -11.11229 -1.57173
user_004 Jumping 1.446046442761e12 -2.14534 -2.79678 -2.0699
user_004 Jumping 1.446046444187e12 -1.8771 1.57173 -1.80165
user_004 Jumping 1.446046444899e12 0.498763 1.30349 1.18733
user_004 Jumping 1.446046445222e12 -0.267643 3.2195 -2.10822
user_004 Jumping 1.446046445352e12 1.61005 -0.689167 -0.613724
user_004 Jumping 1.446046445417e12 0.230521 0.958607 -0.805325
user_004 Jumping 1.446046446193e12 -1.26397 0.805325 1.18733
user_004 Jumping 1.446046446517e12 0.652044 0.268841 0.995729
user_004 Jumping 1.446046446712e12 -2.10702 -2.18366 4.06135
user_004 Jumping 1.446046447036e12 0.498763 0.690364 -1.34181
user_004 Jumping 1.446046448849e12 -0.535886 -3.83143 4.63616
user_004 Jumping 1.446046449367e12 2.56806 -8.08499 1.41725
user_004 Jumping 1.446046451892e12 -0.382604 0.690364 7.6042e-2
user_004 Jumping 1.446046452215e12 -7.6042e-2 3.44943 -2.2615
user_004 Jumping 1.446046452538e12 18.54763 -15.40417 -3.98591
user_004 Jumping 1.446046452668e12 -3.7722e-2 -5.40257 3.67815
user_004 Jumping 1.446046453445e12 3.0279 -1.45557 -7.7239e-2
user_004 Jumping 1.446046453575e12 -0.305964 0.690364 -1.07357
user_004 Jumping 1.44604645364e12 8.31611 -4.5212 0.497565
user_004 Jumping 1.446046453834e12 1.18853 5.05888 0.344284
user_004 Jumping 1.44604645487e12 12.22478 -14.1396 -1.03525
user_004 Jumping 1.44604645623e12 1.41845 -3.71647 -0.958607
user_004 Jumping 1.446046456488e12 18.58595 -16.28553 -4.714
user_004 Jumping 1.446046456813e12 0.881966 -0.765807 -0.1922
user_006 Walking 1.446046893889e12 -3.33327 -5.40257 -3.60271
user_006 Walking 1.446046894277e12 -5.70913 -6.36057 -2.29982
user_006 Walking 1.446046895636e12 -8.96635 -10.001 -1.99325
user_006 Walking 1.446046895895e12 -5.44089 -7.05034 -1.76333
user_006 Walking 1.446046896218e12 -6.51385 -11.11229 -2.98958
user_006 Walking 1.446046896477e12 -5.70913 -5.21096 -2.03158
user_006 Walking 1.446046896607e12 -6.16897 -6.93538 -2.0699
user_006 Walking 1.446046896865e12 -4.67448 -9.57948 -0.307161
user_006 Walking 1.446046898354e12 -8.35323 -8.50651 -6.55337
user_006 Walking 1.446046898872e12 -8.54483 -9.6178 -1.80165
user_006 Walking 1.446046899908e12 -6.9737 -8.85139 -0.958607
user_006 Walking 1.446046899973e12 -9.4262 -10.15428 -1.76333
user_006 Walking 1.446046900361e12 -3.37159 -4.40624 -2.98958
user_006 Walking 1.446046902044e12 -7.12698 -8.69811 -1.22685
user_006 Walking 1.446046903274e12 -5.51753 -9.15796 -1.38013
user_006 Walking 1.446046903727e12 -8.04667 -7.62514 -7.66466
user_006 Walking 1.446046906122e12 -7.01202 -6.89706 -0.843646
user_006 Walking 1.446046907157e12 -6.28393 -7.43354 -0.345482
user_006 Walking 1.446046908906e12 -2.91174 -3.67815 -2.68302
user_006 Walking 1.446046910005e12 -2.72014 -4.138 -2.60638

Feature Selection on Running Windows

  1. ETL Using SparkSQL Windows

A Markov Process Assumption

This is sensible since the subjects are not instantaneously changing between the activities of interest: sitting, walking, jogging, etc. Thus it makes sense to try and use the most recent accelerometer readings (from the immediate past) to predict the current activity.

 // Import the window functions.
import org.apache.spark.sql.expressions.Window
import org.apache.spark.sql.functions._

// Create a window specification
val windowSize = 10
val wSpec1 = Window.partitionBy("user_id","activity").orderBy("timeStampAsLong").rowsBetween(-windowSize, 0)
import org.apache.spark.sql.expressions.Window
import org.apache.spark.sql.functions._
windowSize: Int = 10
wSpec1: org.apache.spark.sql.expressions.WindowSpec = org.apache.spark.sql.expressions.WindowSpec@184df46f
 // Calculate the moving window statistics from data
val dataFeatDF = dataDF
      .withColumn( "meanX", mean($"x").over(wSpec1)  )
      .withColumn( "meanY", mean($"y").over(wSpec1)  )
      .withColumn( "meanZ", mean($"z").over(wSpec1)  ) 
//resultant = 1/n * ∑ √(x² + y² + z²)
      .withColumn( "SqX", pow($"x",2.0) )
      .withColumn( "SqY", pow($"y",2.0) )
      .withColumn( "SqZ", pow($"z",2.0) )
      .withColumn( "resultant", pow( $"SqX"+$"SqY"+$"SqZ",0.50 ) )
      .withColumn( "meanResultant", mean("resultant").over(wSpec1) )
// (1 / n ) * ∑ |b - mean_b|, for b in {x,y,z} 
      .withColumn( "absDevFromMeanX", abs($"x" - $"meanX") )
      .withColumn( "absDevFromMeanY", abs($"y" - $"meanY") )
      .withColumn( "absDevFromMeanZ", abs($"z" - $"meanZ") )
      .withColumn( "meanAbsDevFromMeanX", mean("absDevFromMeanX").over(wSpec1) )
      .withColumn( "meanAbsDevFromMeanY", mean("absDevFromMeanY").over(wSpec1) )
      .withColumn( "meanAbsDevFromMeanZ", mean("absDevFromMeanZ").over(wSpec1) )
//standard deviation  = √ variance = √ 1/n * ∑ (x - u)² with u = mean x
      .withColumn( "sqrDevFromMeanX", pow($"absDevFromMeanX",2.0) )
      .withColumn( "sqrDevFromMeanY", pow($"absDevFromMeanY",2.0) )
      .withColumn( "sqrDevFromMeanZ", pow($"absDevFromMeanZ",2.0) )
      .withColumn( "varianceX", mean("sqrDevFromMeanX").over(wSpec1) )
      .withColumn( "varianceY", mean("sqrDevFromMeanY").over(wSpec1) )
      .withColumn( "varianceZ", mean("sqrDevFromMeanZ").over(wSpec1) )
      .withColumn( "stddevX", pow($"varianceX",0.50) )
      .withColumn( "stddevY", pow($"varianceY",0.50) )
      .withColumn( "stddevZ", pow($"varianceZ",0.50) )
dataFeatDF: org.apache.spark.sql.DataFrame = [user_id: string, activity: string ... 27 more fields]
display(dataFeatDF.sample(false,0.1))
user_id activity timeStampAsLong x y z meanX meanY meanZ SqX SqY SqZ resultant meanResultant absDevFromMeanX absDevFromMeanY absDevFromMeanZ meanAbsDevFromMeanX meanAbsDevFromMeanY meanAbsDevFromMeanZ sqrDevFromMeanX sqrDevFromMeanY sqrDevFromMeanZ varianceX varianceY varianceZ stddevX stddevY stddevZ
user_001 Jogging 1.446047139921e12 2.2615 -11.34221 1.11069 4.769736363636363 -9.105701545454545 -0.27929245454545465 5.114382249999999 128.6457276841 1.2336322760999998 11.618680743105045 12.494198224372735 2.508236363636363 2.2365084545454543 1.3899824545454547 3.004076849075167 6.053738699439197 2.006725409359832 6.291249655867765 5.001970067253296 1.932051223944207 13.276512488367912 55.13839612187212 6.2454340102018895 3.6436948950711985 7.4255232894303225 2.499086635193324
user_001 Jogging 1.446047140245e12 -1.34061 -19.58108 3.21831 2.0873136363636364 -7.7122354545454535 -0.18871709090909092 1.7972351721000002 383.4186939664 10.357519256099998 19.889028342143813 12.629144725518342 3.4279236363636363 11.868844545454547 3.4070270909090907 4.753278789846518 7.574200039521841 2.467566211839171 11.750660456740496 140.86947084416613 11.607833598188462 42.19660591740247 77.92220654221632 8.576921435389462 6.495891464410598 8.827355580365861 2.9286381537140196
user_001 Jogging 1.446047140569e12 4.63736 -15.05928 0.420925 2.9826163636363634 -7.151363545454545 0.23280709090909094 21.505107769600002 226.78191411839998 0.177177855625 15.762747214354006 13.153262839097122 1.6547436363636367 7.907916454545455 0.18811790909090906 6.333303553719008 7.918052239669422 2.1468873636363637 2.7381765020859516 62.53514265207075 3.538834772073553e-2 59.6090899788082 81.98783760943543 7.147677048385896 7.720692325096772 9.054713557558594 2.6735139888143276
user_001 Jogging 1.446047141021e12 1.49509 -19.54276 4.67448 3.167250909090909 -7.496246999999999 -0.2270356363636364 2.2352941081 381.91946841760006 21.850763270399998 20.14957879947122 11.485779570157224 1.6721609090909089 12.046513000000001 4.901515636363636 5.198262314049587 8.112503272727274 2.16874 2.796122105891735 145.11847545916902 24.024855533517222 35.721060701640276 78.69404505664698 7.111298197847909 5.976709855902349 8.870966410524108 2.666701745199097
user_001 Jogging 1.446047141216e12 9.50404 0.805325 -1.91661 3.8500481818181824 -9.464517545454546 -0.1190421818181818 90.3267763216 0.6485483556249999 3.6733938920999996 9.728757298305112 13.021301578961113 5.653991818181817 10.269842545454546 1.7975678181818182 5.054480909090909 7.997542595041323 2.5874130247933884 31.96762348006693 105.46966590842831 3.2312500609629424 29.863606153648753 78.64192339576647 9.26849699920601 5.464760393068369 8.86802815713654 3.0444206344074747
user_001 Jogging 1.446047142279e12 1.87829 -12.83671 4.29128 3.6758644545454544 -10.067191818181819 1.783038181818182 3.5279733241 164.7811236241 18.415084038400003 13.66470566776321 15.459400519749591 1.7975744545454544 2.7695181818181815 2.5082418181818182 3.7047198760330575 8.578998289256198 2.3112528677685953 3.231273919634388 7.670230959421486 6.291277018476033 30.205942270589105 97.09991623522866 7.76694319591596 5.49599329244397 9.85392897453745 2.786923607836419
user_001 Jogging 1.446047142286e12 1.38013 -11.03565 1.37893 3.4668444545454546 -9.293818181818182 1.6924627272727273 1.9047588169000003 121.78557092250001 1.9014479449 11.206773741104083 14.657520425434432 2.0867144545454543 1.7418318181818186 0.3135327272727273 3.8557840495867763 7.7102990413223145 2.1829909090909094 4.354377214808933 3.03397808283058 9.83027710710744e-2 30.585373629779973 85.7726380372951 7.505552122014648 5.530404472530013 9.261351847181658 2.739626274150299
user_001 Jogging 1.446047142375e12 -4.06135 3.94759 -2.8363 -1.413767909090909 -1.8387784545454544 0.4244077272727273 16.4945638225 15.583466808099999 8.04459769 6.334242521454321 5.009300086899544 2.647582090909091 5.786368454545454 3.2607077272727274 2.194390801652892 5.256532165289254 1.5008256694214879 7.009690928102553 33.482059891758745 10.632214882696076 6.146341433895125 32.61759539584144 3.5185498123723344 2.4791816056705334 5.711181611176573 1.875779787814213
user_001 Jogging 1.446047142383e12 -4.09967 5.71033 -4.63736 -1.9154151818181817 -0.5567893636363634 -0.11904409090909084 16.8072941089 32.6078687089 21.505107769600002 8.421417374017274 4.991653538371555 2.184254818181818 6.267119363636363 4.5183159090909095 2.257413231404958 5.807901942148759 1.9014471157024795 4.770969110750487 39.27678511806585 20.41517865434401 6.3779654324036805 36.18450086682646 5.373345345458154 2.525463409436708 6.0153554231505275 2.3180477444302467
user_001 Jogging 1.446047142554e12 -4.138 -13.29655 -19.54396 3.766440545454545 -2.9570327272727273 -2.857203727272727 17.123044 176.7982419025 381.96637248159993 23.997659435538708 9.403610514754291 7.904440545454545 10.339517272727273 16.686756272727273 5.648922247933883 4.328929578512397 5.261284214876033 62.48018033662574 106.90561743302561 278.447834905403 40.53182288476939 26.28204059887057 49.8798457427616 6.366460781687843 5.126601271687761 7.0625665124486865
user_001 Jogging 1.446047142594e12 1.87829 -19.58108 1.57053 6.187586363636364 -8.304458454545456 0.2293225454545458 3.5279733241 383.4186939664 2.4665644809 19.73355598394268 16.627602201403956 4.309296363636364 11.276621545454544 1.3412074545454542 5.647655338842975 5.920330975206611 9.059428404958679 18.570035149649595 127.16219347940964 1.7988374361282966 42.971910058386946 51.737361373205154 117.22960161633895 6.555296336428045 7.192868786041155 10.827261963042131
user_001 Jogging 1.446047142691e12 13.56599 -19.58108 2.41358 5.995984909090908 -19.581079999999996 3.625896636363636 184.03608468009998 383.4186939664 5.8253684164 23.943269347833432 22.646530680721458 7.570005090909091 3.552713678800501e-15 1.212316636363636 6.413111057851239 2.7400603553719036 5.932997801652892 57.304977076389555 1.2621774483536189e-29 1.4697116268040404 53.08331806979702 14.682762675546309 41.69279164792213 7.285829950650579 3.831809321397179 6.456995558920737
user_001 Jogging 1.446047142708e12 7.9329 -19.54276 4.36792 7.382483636363636 -19.57759636363636 2.2672675454545446 62.93090241 381.91946841760006 19.0787251264 21.539013346808623 22.445030614743192 0.5504163636363639 3.483636363635867e-2 2.1006524545454552 6.184139041322314 1.4485709917355396 4.827092694214876 0.30295817335867803 1.2135722314046127e-3 4.412740734787846 51.846041086663654 5.329512547258234 30.756938086205707 7.2004195076859 2.3085737040991856 5.545893804086561
user_001 Jogging 1.446047142748e12 5.90193 -11.15061 0.574206 8.772467272727276 -17.264443636363637 1.7830378181818183 34.8327777249 124.33610337210001 0.329712530436 12.629275261369356 19.990844360519667 2.870537272727276 6.113833636363637 1.2088318181818183 6.053026280991736 1.8675605785123965 3.4662473884297524 8.239984234116548 37.37896173313141 1.4612743646487605 48.73046402970053 9.197896057389853 18.544546604793048 6.9807208818073025 3.032803333121001 4.306337957568245
user_001 Jogging 1.44604714278e12 8.08618 -5.05768 -6.66833 6.333900909090909 -13.038758181818183 0.9434755454545454 65.38630699240001 25.580126982400003 44.4666249889 11.637571007890779 15.478486935501174 1.7522790909090915 7.981078181818183 7.611805545454546 2.751777404958678 4.34032950413223 3.3056813305785124 3.0704820124371923 63.69760894429423 57.93958366181258 11.526650756635524 26.58225658028617 15.31464409781463 3.3950921573111272 5.155798345580068 3.913392913804418
user_001 Jogging 1.446047142805e12 8.35443 1.15021 -5.71033 6.549888181818181 -8.025764454545454 -2.087313545454545 69.7965006249 1.3229830441 32.6078687089 10.184662605010537 12.622237469497941 1.8045418181818196 9.175974454545454 3.623016454545455 2.6760871900826455 6.690536685950412 4.164880024793389 3.256371173566947 84.19850719047074 13.126248229907118 10.786670222573182 48.26457948474828 22.346682708536058 3.2843066578157987 6.947271369735623 4.727227803748837
user_001 Jogging 1.446047142829e12 7.62634 5.44208 -4.44576 7.870197272727273 -2.8978099090909075 -4.320343545454545 58.1610617956 29.6162347264 19.7647819776 10.370249683570787 11.335677718498262 0.24385727272727298 8.339889909090907 0.12541645454545503 1.4216515702479346 7.973158644628099 3.7759768181818187 5.9466369461983595e-2 69.55376369575633 1.5729287070752187e-2 2.692849359760634 65.2374106261797 21.077675670898802 1.6409903594356166 8.076967910433945 4.591042982906913
user_001 Jogging 1.446047142869e12 0.1922 1.41845 -4.63736 6.093528181818181 2.8014646363636366 -5.215646363636364 3.694084e-2 2.0120004025 21.505107769600002 4.853251385627989 9.218776944004022 5.901328181818181 1.3830146363636366 0.578286363636364 2.520273636363636 6.500834239669422 1.8697786859504135 34.82567430952148 1.912729484396042 0.334415118367769 9.10457395356957 52.70820165063524 8.841695357028382 3.0173786559809774 7.260041435875917 2.9734988409327454
user_001 Jogging 1.446047142886e12 -2.4519 -1.53221 -1.57173 4.240219090909091 2.961713181818182 -4.400469090909092 6.011813610000001 2.3476674841 2.4703351929000004 3.290868621959862 7.8287111805749525 6.692119090909091 4.493923181818182 2.828739090909092 3.319933140495868 5.620416438016528 1.1214241239669427 44.784457926909916 20.195345564082857 8.001764844437195 16.078224532538766 41.51470011538472 2.4825790390895945 4.009766144370363 6.443190212572086 1.5756202077561694
user_001 Jogging 1.446047142918e12 3.8919e-2 -7.5485 2.41358 0.4081871818181817 -0.3059640909090906 -2.2266609090909095 1.514688561e-3 56.97985224999999 5.8253684164 7.925070053631134 6.315034135405699 0.3692681818181817 7.242535909090909 4.64024090909091 4.338746115702478 4.679827628099175 2.179507727272728 0.1363589901033057 52.45432639447129 21.53183569440083 23.128383278630352 26.851247524683767 8.024400492232104 4.809197779113513 5.181818939782031 2.832737279069858
user_001 Jogging 1.446047143048e12 4.86728 -19.58108 0.957409 10.678030909090909 -19.525341818181815 -1.6205011818181818 23.6904145984 383.4186939664 0.9166319932809999 20.19964704043318 22.590165936575104 5.810750909090909 5.573818181818524e-2 2.577910181818182 4.778637975206611 4.502477933884299 1.594884165289256 33.764826127500825 3.1067449123970757e-3 6.645620905521852 25.40047323918317 31.66346295541629 3.9266513036706896 5.0398882169333055 5.627029674296759 1.9815779832423173
user_001 Jogging 1.44604714308e12 3.0279 -19.58108 5.2876 9.615512727272726 -19.556694545454544 8.649336363636362e-2 9.16817841 383.4186939664 27.958713760000002 20.507208150706425 22.28960157670052 6.5876127272727265 2.4385454545456042e-2 5.201106636363637 5.043396785123966 1.4739062809917371 1.867876578512397 43.396641444525606 5.946503933885027e-4 27.051510242825863 28.349099778321065 5.239003576490311 5.987174106897974 5.324387267876094 2.2888869732886135 2.4468702676884964
user_001 Jogging 1.446047143153e12 4.25415 -0.612526 0.727487 1.9828029090909092 -11.161062363636363 3.841882454545454 18.0977922225 0.375188100676 0.529237335169 4.359153318976634 12.602918806903675 2.271347090909091 10.548536363636362 3.114395454545454 4.325445371900826 5.669189173553718 2.3229701652892563 5.15901760738119 111.27161941495865 9.699459047293386 25.218244932986796 46.66018201959887 7.700625972606309 5.02177706922428 6.8308258665844255 2.7750001752443745
user_001 Jogging 1.446047143242e12 -5.74745 4.86728 -1.80165 -3.260111181818182 4.99269 -3.421557272727273 33.0331815025 23.6904145984 3.2459427224999997 7.744000182295968 7.55742066211505 2.4873388181818177 0.12540999999999958 1.6199072727272732 3.4627619504132228 5.632767752066116 3.413991008264463 6.186854396434121 1.5727668099999894e-2 2.6240995722347122 14.443867894436066 49.65072869425762 18.454665286095363 3.8005088994022977 7.0463273195514855 4.295889347515292
user_001 Jogging 1.446047143484e12 6.24681 -19.58108 3.63983 -0.31641409090909084 -19.340707272727265 3.7861454545454545 39.0226351761 383.4186939664 13.248362428899998 20.873181156004947 21.793673526369936 6.563224090909091 0.24037272727273518 0.14631545454545458 4.006847198347107 4.57468519834711 5.562779223140495 43.075910467489464 5.7779048016532726e-2 2.1408212238842986e-2 22.94847834491234 30.761658745192324 62.221786747632834 4.7904570079390485 5.546319387232611 7.888078774177704
user_001 Jogging 1.446047143533e12 11.22845 -19.58108 9.15796 4.856828 -19.581079999999996 3.622413636363636 126.07808940250001 383.4186939664 83.86823136159998 24.359084850020537 22.40485202749899 6.371622 3.552713678800501e-15 5.535546363636364 6.480882214876033 0.7306194214876078 5.342358561983472 40.597566910884005 1.2621774483536189e-29 30.64227354396777 48.619000492080474 1.6596915876648444 41.51160187686411 6.9727326416606905 1.2882901799147755 6.442949780718775
user_001 Jogging 1.44604714363e12 5.82529 3.14286 3.21831 11.935633636363635 -4.315663545454545 -2.742242818181819 33.9340035841 9.877568979600001 10.357519256099998 7.359965476807618 14.48403310791005 6.110343636363635 7.458523545454545 5.960552818181819 4.2234690247933875 8.366494983471073 7.1579815123966934 37.33629935444957 55.629573478099836 35.52818989833523 22.091004368014264 72.82379547301899 68.08732499721447 4.700106846446607 8.53368592537943 8.251504408119436
user_001 Jogging 1.446047143663e12 3.87095 6.05521 0.650847 7.797039090909089 1.4045146363636363 8.300872727272714e-2 14.9842539025 36.6655681441 0.42360181740899994 7.216191784037409 9.495099067442254 3.926089090909089 4.6506953636363635 0.5678382727272728 4.072720743801653 7.843313049586777 4.4008187355371895 15.414175549755356 21.628967365348768 0.3224403039738927 20.156069219244248 65.0230244160993 25.9053624014897 4.489551115562028 8.063685535541381 5.08973107359217
user_001 Jogging 1.446047143687e12 0.805325 5.40376 -1.18853 4.815022272727273 3.9789428181818183 1.4346706363636363 0.6485483556249999 29.2006221376 1.4126035609000003 5.591222947989554 7.279610887559767 4.009697272727273 1.4248171818181818 2.623200636363636 4.808407685950414 5.901961702479338 3.262293380165289 16.07767221891653 2.0301040016043057 6.881181578618586 23.86087788087626 40.88601350062889 14.184341683283828 4.8847597567205145 6.394217192168944 3.7662105203086864
user_001 Jogging 1.446047143816e12 5.25048 -19.58108 3.21831 3.5051649090909094 -14.543700909090909 1.8248400000000002 27.567540230399995 383.4186939664 10.357519256099998 20.526659578531035 15.631401506522486 1.7453150909090902 5.037379090909091 1.3934699999999995 2.619398677685951 9.328620743801652 3.4855632314049587 3.046124766555006 25.375188105528103 1.9417586408999987 8.646362838626812 93.54406741070962 19.849020919530062 2.9404698329734336 9.671818206041179 4.455224003294342
user_001 Jogging 1.446047143849e12 7.24314 -19.58108 3.14167 5.365441818181818 -19.055046363636357 3.281012727272727 52.4630770596 383.4186939664 9.8700903889 21.112836413303164 20.327333710024067 1.8776981818181824 0.5260336363636426 0.139342727272727 2.544658710743802 6.967329090909092 2.8046661157024797 3.525750462003308 0.276711386585957 1.9416395643801578e-2 8.143183079260638 69.0138884550936 12.59461059977295 2.8536263033657083 8.30745980761229 3.5488886429096294
user_001 Jogging 1.446047144019e12 -5.40257 6.66833 -3.06622 -2.521573636363637 1.8539080909090908 -1.5299249090909088 29.187762604899998 44.4666249889 9.4017050884 9.113511545074159 6.109509864671735 2.880996363636363 4.8144219090909095 1.536295090909091 3.2211229834710746 9.29378385950413 2.721057818181819 8.300140047285947 23.17865831873456 2.3602026063513724 10.905233028506162 91.25062469758161 9.55560119495235 3.3023072280613386 9.552519285381297 3.0912135472905056
user_001 Jogging 1.446047144099e12 -1.22565 2.8363 -1.87829 -3.782661818181819 6.0168872727272715 -1.9479664545454547 1.5022179224999999 8.04459769 3.5279733241 3.6159077610746655 7.549696857727938 2.557011818181819 3.1805872727272715 6.967645454545468e-2 1.4640892479338838 1.9907564793388437 1.209148776859504 6.538309438321491 10.116135399434702 4.854808318024812e-3 2.7824785542542148 6.021358653040184 2.015921675846954 1.6680763034868082 2.453845686476675 1.4198315660130092
user_001 Jogging 1.446047144164e12 3.0279 -3.63983 5.47921 2.8641704545454547 0.45695827272727274 -0.5614681818181815 9.16817841 13.248362428899998 30.021742224100002 7.241428247452294 6.395763415462877 0.1637295454545451 4.096788272727273 6.040678181818182 3.994813181818181 3.586591016528926 3.1257973966942147 2.680736405475195e-2 16.78367415155571 36.48979289629421 22.083146815942428 14.230722467376609 13.901029976940652 4.699270881311528 3.7723629819221545 3.728408504568759
user_001 Jogging 1.446047144205e12 11.84158 -9.11964 19.58108 4.177513272727273 -4.695380454545455 2.410097272727273 140.2230168964 83.1678337296 383.4186939664 24.633504513008294 11.547958818299337 7.664066727272727 4.424259545454546 17.170982727272726 5.005709380165289 4.785287421487603 7.658678082644627 58.73791880008889 19.574072525545663 294.8426478202983 30.767078886801734 24.89549485314188 85.72207552243663 5.54680799079991 4.98953854110196 9.258621685890219
user_001 Jogging 1.446047144294e12 11.95654 -19.58108 3.75479 3.0906112727272728 -19.267550909090904 6.416312 142.9588487716 383.4186939664 14.098447944099998 23.248139510122094 21.319530424095966 8.865928727272728 0.3135290909090962 2.6615219999999997 3.267994859504132 5.688191446280993 3.850399157024793 78.60469219707981 9.830049084628431e-2 7.083699356483999 16.635098001876802 45.33735918091032 19.356079423879518 4.078614716037396 6.733302249335783 4.399554457428561
user_001 Jogging 1.446047144318e12 7.51138 -19.58108 9.46452 4.619939454545455 -19.581079999999996 6.872671818181818 56.4208295044 383.4186939664 89.5771388304 23.009056093225553 22.07631496113507 2.891440545454545 3.552713678800501e-15 2.5918481818181824 4.7118147438016535 2.8803568595041344 2.8274684132231402 8.360428427898476 1.2621774483536189e-29 6.717676997594218 29.996919431021933 16.063989735606317 8.899686623597681 5.476944351645535 4.007990735469122 2.983234255568557
user_001 Jogging 1.446047144334e12 2.10822 -19.58108 6.43721 4.919534545454545 -19.581079999999996 6.782096363636364 4.444591568400001 383.4186939664 41.43767258410001 20.71957910091081 22.086492683781803 2.811314545454545 3.552713678800501e-15 0.3448863636363635 4.764385933884298 1.5176105785123994 2.3502069586776853 7.903489473484295 1.2621774483536189e-29 0.11894660382231395 30.15813492282921 5.744719094941251 6.931913594880021 5.49164227921204 2.3968143638882946 2.6328527484232804
user_001 Jogging 1.446047144358e12 0.268841 -14.48448 1.26397 5.449051181818183 -18.745 5.249283636363637 7.2275483281e-2 209.8001608704 1.5976201609 14.542010057573918 20.811476939808895 5.1802101818181825 4.260520000000001 3.9853136363636366 4.9189340495867775 1.0736021487603329 2.2425308925619833 26.83457752781277 18.152030670400013 15.882724780185953 31.661174239479916 3.0665480847950435 6.424955978969012 5.626826302586558 1.751156213704261 2.5347496876356472
user_001 Jogging 1.446047144432e12 11.38173 3.67935 -9.88724 5.041460454545454 -7.349934545454545 -3.8117286363636365 129.5437777929 13.5376164225 97.75751481760001 15.518985438262387 12.73755665238099 6.340269545454545 11.029284545454544 6.075511363636364 3.7813608181818186 7.248872066115704 5.965617710743802 40.19901790901838 121.64511758460246 36.911838329674595 18.001369432075183 58.53190460909211 39.68507574973153 4.242802073167588 7.650614655639905 6.299609174364036
user_001 Jogging 1.44604714457e12 3.44943 -17.32018 1.49389 2.223177454545455 -5.730029545454546 -0.4325736363636365 11.8985673249 299.98863523240004 2.2317073320999996 17.72340006571538 8.926374908928052 1.2262525454545452 11.590150454545455 1.9264636363636365 1.3424779999999998 5.841155958677685 3.5812076942148754 1.5036953052337514 134.3315875590002 3.7112621422314054 3.7642855529851604 51.2352123894596 17.394233076215162 1.940176680868307 7.157877645605546 4.1706394085577765
user_001 Jogging 1.446047144626e12 3.18118 -19.58108 3.98471 3.6688972727272726 -17.389854545454543 3.542288636363637 10.1199061924 383.4186939664 15.877913784100002 20.234043440274117 18.341820410456116 0.4877172727272727 2.1912254545454566 0.4424213636363632 1.1087558842975207 8.010527595041323 3.06119141322314 0.23786813811652893 4.801468992647943 0.1957366630018591 1.601310337728242 74.55691742125481 15.713996208770943 1.2654289145298687 8.634634758995588 3.964088320001327
user_001 Jogging 1.446047144715e12 5.67201 -9.27292 0.804128 3.6375445454545456 -17.180836363636367 3.099863181818182 32.171697440100004 85.98704532639998 0.646621840384 10.89978736521424 17.99224847571835 2.0344654545454546 7.907916363636367 2.295735181818182 1.2424019008264464 2.141185867768598 1.2177001818181816 4.1390496857388435 62.53514121426783 5.270400025037761 2.150091168155898 11.058832569033141 2.142394874962366 1.466318917615093 3.3254823062276455 1.4636922063611482
user_001 Jogging 1.446047144755e12 1.34181 -2.87342 0.420925 4.045133636363636 -10.513101818181816 1.086304272727273 1.8004540760999999 8.2565424964 0.177177855625 3.1990896248972143 11.680282540342732 2.7033236363636366 7.639681818181817 0.6653792727272729 1.4530048760330578 5.778132809917356 1.9492681322314047 7.307958682922315 58.36473828305783 0.44272957657507467 2.9269021093244927 43.49758092784231 5.312242645339325 1.7108191340186993 6.595269587199776 2.3048302855827205
user_001 Jogging 1.446047144763e12 1.34181 -1.37893 -0.15388 3.578322727272728 -8.858360909090909 1.0096636363636364 1.8004540760999999 1.9014479449 2.3679054399999996e-2 1.9301764363394347 9.979759335687318 2.2365127272727277 7.479430909090908 1.1635436363636364 1.4216519008264463 6.458081074380166 1.7788850743801652 5.001989179252894 55.94188672386445 1.3538337937223142 2.7758463535522164 48.58320699364817 4.596412149495224 1.6660871386431793 6.970165492558134 2.1439244738318615
user_001 Jogging 1.446047144917e12 6.59169 2.10822 2.2603 -1.190814909090909 5.494338181818182 -3.383237818181818 43.450377056099995 4.444591568400001 5.1089560899999995 7.280379434789096 8.801927778002462 7.782504909090909 3.3861181818181816 5.643537818181818 2.3958118512396696 2.5212229090909086 4.374532033057851 60.567382660024094 11.465796341239669 31.84951910524839 11.386474285730058 7.176292284465379 34.127908503264536 3.3743850233383355 2.678860258480345 5.8419096623676525
user_001 Jogging 1.446047144965e12 -1.49389 -10.80573 -8.50771 1.8608763636363634 -1.807423636363636 -0.2583900000000001 2.2317073320999996 116.76380083290002 72.3811294441 13.833894520672768 10.624124936163746 3.3547663636363634 8.998306363636365 8.249319999999999 3.971061611570248 5.76831652892562 7.454093057851239 11.254457354585949 80.9695174138587 68.05128046239999 21.70051268411826 45.90407271894876 64.16546233071315 4.658380908010664 6.775254439425043 8.010334720266885
user_001 Jogging 1.446047145046e12 -4.17632 -19.58108 5.82409 2.0176396363636364 -16.04516 3.5074527272727267 17.441648742399998 383.4186939664 33.9200243281 20.85138765254965 19.917295300480387 6.193959636363636 3.535920000000001 2.3166372727272733 3.7306884876033055 6.614528264462811 5.751531818181817 38.365135976901946 12.502730246400006 5.366808253389259 18.671942642803675 48.08396713180992 68.08284963383029 4.321104331395352 6.934260388232469 8.251233218969773
user_001 Jogging 1.446047145095e12 8.39275 -19.58108 7.77842 3.1184786363636365 -19.581079999999996 5.907696363636364 70.4382525625 383.4186939664 60.50381769639999 22.679523015824206 21.447303073035563 5.2742713636363625 3.552713678800501e-15 1.8707236363636355 5.020279380165289 3.0450398347107455 1.37161479338843 27.817938417274576 1.2621774483536189e-29 3.4996069236495835 31.002898462194388 16.330388050525777 2.60981791889955 5.568024646335035 4.041087483651619 1.6154930884716128
user_001 Jogging 1.446047145232e12 4.36911 2.49142 -3.2195 5.825286363636365 -4.29824409090909 -3.8256609090909084 19.0891221921 6.207173616400001 10.36518025 5.971723039332953 9.514844653794894 1.4561763636363647 6.78966409090909 0.6061609090909084 2.2583658925619834 7.407538256198347 3.772808876033058 2.120449602013226 46.09953846738036 0.36743104770991647 6.742655839755869 55.6615513466919 18.947554227282133 2.596662442397138 7.460666950527406 4.3528788436254615
user_001 Jogging 1.446047145249e12 2.68302 3.33447 -2.22318 5.675488181818182 -1.6436913636363633 -4.062549999999999 7.1985963204 11.1186901809 4.9425293124000005 4.82284312555364 8.220254896054264 2.9924681818181824 4.978161363636364 1.8393699999999988 2.574429280991736 7.315063049586775 3.0010186446280986 8.954865819194218 24.782090562401862 3.3832819968999956 8.001432070676456 54.618597304993834 13.682063792776631 2.828680270139497 7.390439588075518 3.698927384090776
user_001 Jogging 1.446047145289e12 2.18486 2.91294 -0.383802 3.344915454545455 2.4565831818181816 -1.9967373636363634 4.7736132196000005 8.485219443599998 0.147303975204 3.6614391485321724 5.247410582023297 1.160055454545455 0.4563568181818183 1.6129353636363635 2.197559173553719 4.748552677685951 1.925832396694215 1.345728657620662 0.20826154550103315 2.601560487268768 5.862908678780401 29.34863687704508 4.891628359301945 2.4213443949137843 5.417438220879411 2.211702592868658
user_001 Jogging 1.446047145346e12 4.56072 -3.83143 -0.575403 3.031387272727273 1.1571758181818181 -2.355556272727273 20.8001669184 14.6798558449 0.331088612409 5.984238579444255 5.171036039387004 1.529332727272727 4.988605818181818 1.780153272727273 1.7041447107438017 2.1861589338842973 2.350839826446281 2.3388585907074373 24.886188009197486 3.168945674401621 3.740026841003832 6.758621840631681 6.766600337218634 1.9339149001452551 2.599734955842938 2.6012689859410223
user_001 Jogging 1.446047145411e12 4.9056 -19.58108 3.17999 3.7490218181818182 -10.565356818181819 0.7727747272727273 24.064911359999996 383.4186939664 10.1123364001 20.435164343026457 12.227556908045916 1.1565781818181815 9.015723181818181 2.4072152727272726 1.0450998347107436 7.69731570247934 2.7729970082644626 1.3376730906578504 81.28326449117375 5.794685369251438 1.3881511997852738 67.60655777999472 9.645998022142622 1.178198285427913 8.222320705250722 3.1058007054771917
user_001 Jogging 1.446047145476e12 7.77962 -19.58108 -1.03525 6.636979999999999 -19.46611909090909 1.3510629090909094 60.522487344400005 383.4186939664 1.0717425625 21.095329432680117 20.728654720814475 1.142640000000001 0.11496090909091095 2.3863129090909094 2.049979173553719 4.984490190082647 1.4200686280991737 1.3056261696000022 1.321601061900869e-2 5.694489300093919 5.392577351311795 40.45396663996184 2.8114859492491036 2.322192358809191 6.360343280040932 1.6767486243468648
user_001 Jogging 1.446047145516e12 3.14286 -16.13225 0.497565 6.7345227272727275 -19.17697454545454 0.27809427272727266 9.877568979600001 260.24949006249994 0.24757092922499999 16.443072400598524 20.407458939320875 3.5916627272727273 3.0447245454545424 0.21947072727272732 2.3327892561983465 1.3263262809917373 1.124907140495868 12.900041146480165 9.27034755769337 4.8167400129619856e-2 6.693568337809316 3.786078162143052 1.979100510279392 2.5871931388687077 1.9457847162887913 1.4068050718843006
user_001 Jogging 1.446047145713e12 0.537083 1.95493 -9.00587 -1.1315915454545455 6.368736363636364 -1.8399748181818183 0.28845814888899995 3.8217513049000003 81.1056944569 9.231246064897684 8.221043321888848 1.6686745454545455 4.413806363636364 7.165895181818182 1.1534087933884298 4.5578994545454545 3.6043262396694216 2.7844747386479343 19.48168661567686 51.35005375680503 1.7265291963441747 27.517037854864906 22.455774584975515 1.3139745797937548 5.245668485032666 4.7387524291711545
user_001 Jogging 1.446047145793e12 11.07517 -5.55585 15.28921 5.438599363636363 -4.371401454545455 0.483630909090909 122.6593905289 30.867469222500006 233.75994242410002 19.679603709818448 13.06356743224656 5.636570636363637 1.1844485454545453 14.805579090909092 4.959471123966942 6.52902056198347 8.533394933884297 31.770928538716777 1.402918356829388 219.2051722171645 31.199410662336536 50.721947861364015 88.07356490656394 5.585643263075125 7.121934278085134 9.384751723224431
user_001 Jogging 1.446047145842e12 -2.4519 -19.58108 7.1653 3.7977930909090905 -14.17095 3.6642172727272726 6.011813610000001 383.4186939664 51.34152409 20.99457148089477 18.45474752731835 6.249693090909091 5.4101300000000005 3.5010827272727276 3.4136741074380157 7.961440264462809 6.744692446280993 39.05866373055682 29.269506616900006 12.25758026320744 15.41577004773268 71.44910455936972 68.57680084938416 3.9262921500739956 8.452757216398075 8.281111087854343
user_001 Jogging 1.446047145882e12 3.41111 -19.58108 3.33327 1.4741900000000001 -18.839059999999996 6.4372145454545455 11.635671432099999 383.4186939664 11.1106888929 20.153537016896067 20.81950972711309 1.9369199999999998 0.7420200000000037 3.1039445454545453 3.82664652892562 5.608066132231406 3.3576199173553722 3.7516590863999992 0.5505936804000054 9.634471741257023 19.101262520859095 41.887305489479154 18.40387396009669 4.370499115760017 6.472040287998766 4.289973654942031
user_001 Jogging 1.446047146037e12 7.1665 1.99325 -1.99325 5.05887909090909 -6.590495181818182 5.1656545454545434e-2 51.35872225 3.9730455625 3.9730455625 7.70096184739283 9.618719497689767 2.10762090909091 8.583745181818182 2.044906545454545 1.275970876033058 6.988546834710745 0.8360788925619833 4.442065896437193 73.68068134638686 4.181642779642842 2.080890254091703 51.76374093133398 1.196293165590975 1.4425291172422492 7.194702282327878 1.0937518756971232
user_001 Jogging 1.446047146069e12 10.69197 7.24314 -6.66833 6.960960909090908 6.678845454545429e-2 -1.9758360000000001 114.31822248089999 52.4630770596 44.4666249889 14.534370455214082 9.05266860963471 3.731009090909091 7.176351545454546 4.692494 2.112051570247934 8.11630508264463 2.00785705785124 13.920428836446282 51.50002150394785 22.019499940036 5.017466863377312 66.23105049371274 6.894872401938625 2.2399702818067277 8.138246155881053 2.625808904307133
user_001 Jogging 1.446047146101e12 5.13552 2.8363 -2.2615 7.699498181818182 3.8883675454545457 -2.9965497272727273 26.373565670399998 8.04459769 5.114382249999999 6.287491201616111 9.403020285750388 2.5639781818181824 1.0520675454545456 0.7350497272727274 2.158606198347108 6.178120487603305 2.2564640578512396 6.573984116839672 1.1068461201987525 0.5402981015637109 5.51196412323629 47.76565157080517 7.256989296208922 2.347757253899195 6.911269895670778 2.693879970638804
user_001 Jogging 1.446047146133e12 3.64103 -0.727487 -4.44576 6.7345227272727275 3.700250636363637 -3.9162381818181817 13.257099460900001 0.529237335169 19.7647819776 5.792332757505305 8.94416098242155 3.0934927272727273 4.427737636363637 0.5295218181818182 2.5373752066115705 4.200032082644628 1.8229071818181821 9.569697253689256 19.604860576471047 0.2803933559305785 7.398827288804058 24.31675077202084 6.172232880943373 2.7200785446019857 4.93120175738337 2.4843978910277986
user_001 Jogging 1.446047146142e12 2.49142 -2.22198 -3.41111 6.225908181818181 3.0348706363636366 -3.9092709090909086 6.207173616400001 4.937195120399999 11.635671432099999 4.772844033582074 8.453049060126027 3.734488181818181 5.2568506363636365 0.4981609090909087 2.676405371900827 3.922289024793389 1.6018522727272726 13.946401980139665 27.63447861303677 0.24816429134628062 8.224617051718033 20.548089963168977 5.414473050834811 2.867859315189299 4.533000106239683 2.3269020286283673
user_001 Jogging 1.446047146149e12 1.72501 -3.37159 -1.61005 5.49433818181818 2.1395688181818184 -3.44246 2.9756595001 11.3676191281 2.5922610025 4.11528123348818 7.597571407497298 3.76932818181818 5.511158818181818 1.83241 2.7109253719008266 3.6952176198347115 1.2705879421487603 14.207834942248745 30.372871519223217 3.3577264081000004 8.471743534990757 17.478061159130093 2.993352282994137 2.910625969613883 4.1806771173017045 1.7301307126902685
user_001 Jogging 1.446047146182e12 2.49142 -15.59577 2.60518 3.2822109090909093 -3.6851184545454547 -1.6832099999999997 6.207173616400001 243.2280418929 6.7869628323999995 16.006941567385695 7.485217674617422 0.7907909090909091 11.910651545454545 4.28839 2.5221734710743795 5.532376049586777 1.8400089752066116 0.6253502619008264 141.86362023723873 18.390288792099998 7.328542144563707 40.53981984784796 5.562439379226529 2.7071280251520626 6.367088804771609 2.3584824314008634
user_001 Jogging 1.446047146271e12 5.74865 -19.58108 -0.307161 5.564010909090908 -19.452184545454543 0.41047318181818165 33.04697682249999 383.4186939664 9.434787992100001e-2 20.409802024243668 20.332815201913306 0.18463909090909159 0.12889545454545726 0.7176341818181817 1.7611500826446287 5.651453752066117 1.715229809917355 3.4091593891735786e-2 1.6614038202480037e-2 0.5149988189138511 4.313352366296018 51.02793158470397 3.854774185943344 2.076861181277174 7.143383762944839 1.9633578853442244
user_001 Jogging 1.446047146336e12 4.02423 -12.0703 7.6042e-2 4.881213636363636 -18.114457272727275 -0.2374875454545454 16.1944270929 145.69214208999998 5.782385764e-3 12.723692528848062 18.79045997030551 0.8569836363636361 6.044157272727276 0.31352954545454537 1.1033715702479336 1.3883985123966964 0.7727395950413221 0.7344209529950408 36.53183713746202 9.830077587293383e-2 1.4202792273080385 5.608324464644631 1.0397245837182336 1.1917546841980686 2.36819012426043 1.0196688598355026
user_001 Jogging 1.446047146384e12 -1.22565 -3.79311 -0.345482 2.494902636363636 -11.060036363636364 -0.7112660909090909 1.5022179224999999 14.387683472099999 0.119357812324 4.001157233466838 11.537486823091678 3.720552636363636 7.2669263636363635 0.36578409090909086 1.9315339504132227 5.419948677685952 0.7800240247933885 13.842511919952402 52.80821877451322 0.13379800116219004 5.13675033189447 37.824145244424585 0.7892765054106935 2.26644001286036 6.150133758254741 0.8884123510007577
user_001 Jogging 1.446047146424e12 -2.37526 0.575403 2.87342 -0.35821918181818174 -4.0334840000000005 0.22235490909090913 5.6418600676 0.331088612409 8.2565424964 3.77219977949326 5.344345142984176 2.017040818181818 4.608887 2.651065090909091 2.71440861983471 6.813098371900828 1.4035992479338844 4.068453662211578 21.241839378769 7.028146116236827 8.305992954492837 47.69968574953315 2.723286739214193 2.882011962933679 6.9064959096153204 1.6502383886015357
user_001 Jogging 1.446047146458e12 -3.7722e-2 2.49142 2.8351 -1.5356972727272726 -0.4696949090909092 1.8213564545454546 1.422949284e-3 6.207173616400001 8.03779201 3.774438842488245 3.68460736360343 1.4979752727272726 2.9611149090909095 1.0137435454545456 2.3204369421487603 5.309738752066116 1.6677247190082645 2.2439299177023466 8.768201504840466 1.0276759759507523 6.8630149024078095 30.7303997650691 3.57256734741414 2.6197356550628936 5.543500677827063 1.890123632838376
user_001 Jogging 1.446047146522e12 1.95493 3.2195 -2.03158 0.6415932727272727 3.174216363636364 0.9469572727272724 3.8217513049000003 10.36518025 4.127317296399999 4.279515025245267 3.9981079876247936 1.3133367272727274 4.528363636363597e-2 2.978537272727272 1.4387527107438016 2.1126830826446277 1.7142794049586776 1.7248533592034385 2.050607722314014e-3 8.871684285025616 2.352517119129482 5.5079197320681335 3.7086289790114004 1.5337917456843617 2.3468957650624653 1.9257800962237097
user_001 Jogging 1.446047146546e12 5.13552 1.72501 -3.56439 1.9862869090909092 3.1951181818181813 -0.714750909090909 26.373565670399998 2.9756595001 12.7048760721 6.4849133565993 4.507092480087424 3.1492330909090906 1.4701081818181814 2.8496390909090907 1.9106310247933884 1.4853064545454548 2.1149014958677683 9.917669060876825 2.1612180662487592 8.120442948437189 3.988080240379295 2.7498252119819964 5.482809105983013 1.9970178367704419 1.6582596937699463 2.3415399005746225
user_001 Jogging 1.446047146571e12 4.63736 -1.49389 -0.11556 3.170733363636364 2.2196927272727276 -1.4498047272727272 21.505107769600002 2.2317073320999996 1.3354113599999998e-2 4.873414533497023 4.965098592601861 1.4666266363636362 3.7135827272727275 1.3342447272727274 2.0088075950413224 1.669623991735537 2.252981991735537 2.1509936904913136 13.790696672298349 1.7802089922550746 4.605097499204145 3.8262273719452935 5.685248493236532 2.1459490905434233 1.9560744801630876 2.3843759127361883
user_001 Jogging 1.446047146878e12 7.5497 4.59904 -2.03158 9.601578181818182 -2.3648095454545466 -2.6621189090909088 56.997970089999995 21.151168921599997 4.127317296399999 9.070637039811482 12.266509876796164 2.051878181818182 6.963849545454546 0.6305389090909088 2.7384758677685945 7.875615661157027 2.8087830991735534 4.210204073021489 48.49520049172749 0.39757931587755335 12.98708863009436 65.10949435063044 14.582447447172575 3.6037603458185674 8.069045442345113 3.8186970876429274
user_001 Jogging 1.446047146894e12 4.59904 5.32712 -2.4531 9.615512727272728 0.519665 -3.080158818181818 21.151168921599997 28.378207494399998 6.01769961 7.452991079157414 11.528459558044117 5.0164727272727285 4.807455 0.6270588181818177 3.450409504132231 7.804042355371902 2.4350809421487605 25.16499862347109 23.111623577025 0.39320276145957794 16.347791421865587 64.35447876626505 13.496922844239998 4.043240213228196 8.022124330017894 3.673815842450462
user_001 Jogging 1.446047146959e12 -0.535886 0.690364 0.689167 2.303301818181818 4.846375818181818 -1.5159943636363635 0.287173804996 0.476602452496 0.47495115388899994 1.1129813167259368 6.126109555918774 2.839187818181818 4.156011818181819 2.2051613636363636 4.69154547107438 3.318032727272727 1.1686108760330578 8.060987466912033 17.272434232866946 4.862736639674587 23.731583464890104 15.101918680113487 1.6301781262528727 4.8715073093335395 3.886118716677797 1.2767842911991332
user_001 Jogging 1.446047146983e12 3.37279 -5.51753 3.44823 1.1153718181818182 2.536705818181819 -0.11904436363636352 11.375712384100002 30.4431373009 11.8902901329 7.328651978222189 5.187779500312943 2.257418181818182 8.05423581818182 3.5672743636363635 4.118008198347107 3.6100269173553725 1.9562364214876033 5.095936847603308 64.87071461488296 12.725446385457222 20.640781581717523 18.8476167174582 4.691012272734492 4.543212693867361 4.341384193717276 2.1658744822206324
user_001 Jogging 1.446047147096e12 11.42005 -19.58108 -3.0279 7.344163636363636 -19.22574545454545 -2.8397851818181823 130.4175420025 383.4186939664 9.16817841 22.869289765510864 20.970475507049734 4.075886363636364 0.35533454545455 0.18811481818181752 2.502220925619835 5.999820628099176 2.605780305785124 16.612849649276864 0.12626263919339167 3.538718481957826e-2 8.992153747846151 54.692642601319115 8.427556686649925 2.9986920061663804 7.395447424011553 2.903025436790027
user_001 Jogging 1.446047147137e12 7.43474 -17.39682 0.459245 8.991937272727275 -19.361609090909088 -2.7039215454545453 55.2753588676 302.64934611240005 0.210905970025 18.924471219826067 21.673241495557797 1.5571972727272758 1.9647890909090862 3.1631665454545455 2.383775785123967 1.5410471074380183 2.245062066115702 2.424863346189266 3.860396171755353 10.005622594282842 8.250315360901206 5.332303207768298 7.447613372994453 2.8723362200308666 2.3091780372609425 2.729031581531158
user_001 Jogging 1.446047147291e12 -5.096 5.40376 0.191003 -2.6330516363636365 0.955122909090909 3.1277306363636366 25.969216 29.2006221376 3.6482146009e-2 7.430095577017095 5.745923703540493 2.4629483636363636 4.4486370909090915 2.9367276363636368 3.6375790661157024 4.76628705785124 2.561125983471075 6.066114641939041 19.790371966612106 8.624369210181953 13.51211838325738 23.052495135020134 7.287400355275503 3.675883347340797 4.801301400143521 2.6995185413839082
user_001 Jogging 1.446047147299e12 -5.13432 6.40009 -2.87462 -3.1730193636363637 1.8434574545454545 2.7096906363636366 26.361241862399996 40.961152008099994 8.2634401444 8.694011388013015 6.184343097734112 1.961300636363636 4.556632545454545 5.584310636363637 3.455794826446281 4.613322495867768 2.9215261900826452 3.8467001862004038 20.76290015429557 31.184525283404046 12.435550685654261 21.401108802699216 9.883802371350505 3.5264076176265076 4.626133245238319 3.143851518655184
user_001 Jogging 1.446047147355e12 3.41111 0.881966 -3.83263 -2.8525222727272723 4.790637818181818 -3.0313875454545456 11.635671432099999 0.7778640251560001 14.6890527169 5.2060146152461 7.462339132871702 6.263632272727272 3.9086718181818174 0.8012424545454544 2.6555029669421484 3.10837867768595 3.824113 39.233089247950616 15.277715382248754 0.6419894709660245 10.58537307420908 12.414674257063336 17.85669599316412 3.2535170314920867 3.523446360747292 4.225718399652788
user_001 Jogging 1.446047147736e12 -2.18366 1.87829 -4.98224 6.058691818181817 2.9164280909090907 -5.292285454545453 4.768370995600001 3.5279733241 24.8227154176 5.754916136426317 9.230739311965165 8.242351818181817 1.0381380909090907 0.3100454545454534 4.265905685950414 4.891699719008265 1.823541669421487 67.9363634946851 1.0777306957963715 9.612818388429681e-2 25.483026403005535 31.63158155332584 5.8424057463163965 5.0480715528809155 5.624196080625731 2.4171068959225606
user_001 Jogging 1.446047147743e12 -4.59784 1.53341 -4.75232 5.348024545454545 3.146349818181818 -5.281834545454545 21.140132665599996 2.3513462280999997 22.5845453824 6.787932253352268 9.309637091395926 9.945864545454544 1.6129398181818182 0.5295145454545445 5.135555644628099 4.338747471074381 1.5869687272727269 98.92022155652973 2.601574857076397 0.28038565384793285 34.462666228033235 26.484506083387938 4.976233791932779 5.8704911402738045 5.146309948243299 2.230747361745112
user_001 Jogging 1.446047147849e12 7.1665 -18.81467 -3.64103 1.3661955454545456 -7.579855363636364 1.4277029999999997 51.35872225 353.99180720889996 13.257099460900001 20.459902954799173 9.189368471935754 5.800304454545454 11.234814636363636 5.068733 3.350967495867769 6.293398710743801 3.3427343553719013 33.64353176541984 126.22105991345057 25.692054225289 13.470611529964833 48.82826791895325 16.2002231833327 3.6702331710621374 6.9877226561271915 4.02495008457654
user_001 Jogging 1.446047148067e12 -3.63983 5.86361 1.37893 -1.493894 -1.0688853636363633 1.0514679090909091 13.248362428899998 34.3819222321 1.9014479449 7.037878416532926 5.108012830374895 2.145936 6.932495363636364 0.32746209090909084 5.126688247933884 7.607690545454546 0.7584883636363636 4.605041316095999 48.05949196683968 0.10723142098255367 29.09375933065228 58.08169441570896 0.6899635360873132 5.393863117530169 7.621134719692925 0.8306404373056451
user_001 Jogging 1.446047148456e12 15.482 -4.44456 -14.83056 5.260932727272727 -12.206161818181817 -1.9409999090909091 239.69232399999999 19.7541135936 219.9455099136 21.895021066607814 16.00252889430085 10.221067272727272 7.761601818181817 12.889560090909091 3.934323636363636 4.666527107438015 4.5835542479338836 104.47021619361651 60.24246278400329 166.14075933715637 22.934490962878886 27.256494774350404 45.20788764888824 4.7889968639454015 5.220775303951551 6.723681108506577
user_001 Jogging 1.446047148618e12 6.40009 -14.40784 4.44456 6.250292727272727 -4.280825272727273 -0.39425281818181795 40.961152008099994 207.5858534656 19.7541135936 16.37989984912301 10.027533534700176 0.14979727272727228 10.127014727272726 4.838812818181818 1.954652314049587 4.081905495867769 4.160129082644629 2.2439222916528792e-2 102.55642728639869 23.41410948940067 7.110492361411645 26.382294292424103 21.12838448437969 2.66655064857423 5.136369758148658 4.596562246329282
user_001 Jogging 1.446047148715e12 13.25943 -19.58108 4.09967 11.325992727272727 -19.563661818181814 3.6816355454545455 175.8124839249 383.4186939664 16.8072941089 24.00080148662123 23.3560518559995 1.9334372727272733 1.741818181818644e-2 0.4180344545454542 3.472263223140496 4.51767934710744 3.3148654049586783 3.7381796875710767 3.033930578514007e-4 0.1747528051871154 15.492212397006087 35.18123736599198 16.896627558972657 3.9360147861772683 5.931377358252633 4.11055076102615
user_001 Jogging 1.446047148869e12 -12.72175 2.0699 -3.06622 -7.5937909090909095 -2.7375616363636364 -0.14342963636363623 161.8429230625 4.28448601 9.4017050884 13.248740097114895 10.998473902827046 5.127959090909091 4.807461636363636 2.9227903636363637 7.836028842975208 7.575704776859505 3.0896938347107437 26.29596443803719 23.111687385108134 8.542703509765587 66.6865304416707 59.766724667649676 12.372987812976406 8.166182121510069 7.730894169994159 3.517525808430751
user_001 Jogging 1.446047148941e12 -5.70913 1.41845 -2.2615 -8.172079090909092 1.7528828181818183 -1.1432400909090907 32.5941653569 2.0120004025 5.114382249999999 6.3024239788671785 10.5019898639832 2.462949090909092 0.33443281818181836 1.118259909090909 5.765783223140496 3.3173993801652886 1.9834706446280992 6.066118224409922 0.11184530987703317 1.2505052242800083 60.86196647578083 18.08946040022318 4.829903946091108 7.80140798034437 4.253170629098153 2.1977042444539956
user_001 Jogging 1.446047148948e12 -3.29495 1.38013 -5.13552 -7.311613636363638 1.8643600909090912 -1.5090246363636362 10.856695502500001 1.9047588169000003 26.373565670399998 6.255798908996356 9.906212785151986 4.016663636363638 0.4842300909090911 3.6264953636363635 5.211563223140495 2.7061745785123965 2.059477876033058 16.133586767685962 0.23447878094182661 13.15146862247604 53.03097794228993 13.387960177970843 5.317635599192631 7.282237152296671 3.658956159613127 2.305999913094671
user_001 Jogging 1.446047149094e12 7.7413 -19.58108 8.19995 7.0828891818181825 -12.133004545454547 5.524493636363636 59.927725689999995 383.4186939664 67.23918000249999 22.596141255951203 19.778463287097466 0.6584108181818173 7.448075454545453 2.6754563636363633 3.3142304132231404 6.506534396694215 10.932690958677686 0.4335048054988501 55.47382797660246 7.158066753722312 18.004113796689182 51.223312981827924 143.1732729431186 4.243125475011219 7.157046386731605 11.965503455480619
user_001 Jogging 1.446047149143e12 11.38173 -19.58108 18.04827 7.53924909090909 -18.473275454545455 6.872672454545454 129.5437777929 383.4186939664 325.74004999289997 28.960361215844667 23.99309396780716 3.8424809090909093 1.1078045454545453 11.175597545454544 3.264192983471074 5.7432970495867774 8.856425851239669 14.764659536728102 1.2272309109297517 124.89398049796962 17.534738231656146 44.04750329577925 115.42028427408805 4.187450087064459 6.636829310429737 10.743383278748276
user_001 Jogging 1.446047149151e12 10.61533 -19.58108 8.31491 7.037601818181818 -19.163040909090906 6.83783609090909 112.6852310089 383.4186939664 69.1377283081 23.77481131961724 24.163151142198014 3.5777281818181823 0.41803909090909386 1.477073909090909 2.891441256198348 5.236898677685951 8.162859975206612 12.800138942976037 0.17475668152810164 2.1817473329170993 13.339147160653248 40.80328224402284 108.08001828626712 3.6522797210308586 6.387744691518505 10.39615401416635
user_001 Jogging 1.446047149159e12 9.27412 -19.58108 2.95007 7.236170909090908 -19.23271454545454 5.32592609090909 86.0093017744 383.4186939664 8.702913004900001 21.866204717456114 23.59957183787027 2.037949090909092 0.3483654545454584 2.37585609090909 2.9997523223140505 4.254188760330579 6.8035970247933895 4.153236497137195 0.12135848992066385 5.644692164709821 13.651567880630706 29.495691271576558 81.29763851446782 3.694802820263986 5.430993580513289 9.016520310766666
user_001 Jogging 1.446047149523e12 12.79958 -19.58108 -1.99325 15.234664545454546 -19.581079999999996 1.622790272727273 163.82924817640003 383.4186939664 3.9730455625 23.478095913112288 25.618920731320905 2.4350845454545453 3.552713678800501e-15 3.6160402727272727 5.13745561983471 3.858000157024797 4.932868305785124 5.92963674351157 1.2621774483536189e-29 13.07574725398553 33.41003256049624 28.645617400991785 37.17574199616442 5.780141223231163 5.352160068700467 6.097191320285465
user_001 Jogging 1.446047149563e12 3.98591 -15.74905 2.95007 11.92169909090909 -19.128203636363637 0.5080178181818181 15.8874785281 248.0325759025 8.702913004900001 16.511298175355567 23.144901652304863 7.93578909090909 3.379153636363636 2.442052181818182 5.774967107438017 0.8791501652892587 3.5599889008264465 62.97674849539172 11.418679298149584 5.963618858722944 41.11842897361307 2.1366249748332855 16.233832526013103 6.412365318165604 1.4617198687960993 4.029123046769992
user_001 Jogging 1.446047149685e12 -8.96635 0.307161 0.919089 -6.893574181818181 -2.5215752727272727 -4.082363636363617e-3 80.3954323225 9.434787992100001e-2 0.8447245899210001 9.018564452968223 8.545217563577793 2.072775818181819 2.828736272727273 0.9231713636363637 5.534592785123967 5.788583925619835 2.250131214876033 4.29639959243931 8.001748900642985 0.8522453666382231 33.3850424263692 36.61460580992789 7.356495611869291 5.77797909535585 6.051000397448995 2.712286049049637
user_001 Jogging 1.44604714979e12 12.2631 1.03525 -12.87622 -0.8424509090909097 1.226849090909091 -4.585100454545454 150.38362161 1.0717425625 165.7970414884 17.811580661493803 8.372394787765712 13.10555090909091 0.191599090909091 8.291119545454546 4.821074049586776 0.8218279752066114 4.478725966942149 171.7554646307736 3.671021163719011e-2 68.7426633170184 36.154911444741394 0.9207269402372962 42.2056841224175 6.012895429386861 0.9595451736303487 6.496590191971285
user_001 Jogging 1.446047149823e12 6.47673 -5.51753 3.25663 5.142486363636363 1.4533363636363655e-2 -5.609298181818182 41.9480314929 30.4431373009 10.6056389569 9.110258380018648 11.598371733840915 1.3342436363636372 5.532063363636364 8.865928181818182 6.808348099173553 1.6062858842975205 6.176854107438017 1.7802060811768616 30.60372505928768 78.60468252515786 68.21052244459113 5.486770549778637 54.33045585514098 8.258966184976854 2.3423856535119567 7.37091960715493
user_001 Jogging 1.446047149846e12 -7.6042e-2 -8.54483 -3.18118 6.117913545454544 -3.085928 -3.477294181818182 5.782385764e-3 73.01411972889998 10.1199061924 9.118103328382716 14.170774292178116 6.1939555454545445 5.458901999999999 0.29611418181818205 8.038082157024792 3.8665507438016533 8.655006363636364 38.365085299067104 29.799611045603992 8.768360867385137e-2 78.59189304798379 26.740223951981918 99.63844021386738 8.865206881285049 5.171095043797002 9.981905640400903
user_001 Jogging 1.446047149871e12 11.15181 -15.21256 16.7837 8.31958990909091 -6.768160727272726 -0.6938469090909084 124.36286627609998 231.4219817536 281.69258569 25.248315463010595 16.46430774422488 2.8322200909090895 8.444399272727274 17.477546909090908 7.11934505785124 5.128903884297521 8.724047438016528 8.021470643349092 71.30787907723692 305.46464595947316 68.9577918733565 37.06629125091457 114.16631974726042 8.304082843599074 6.088209199010376 10.684864049077106
user_001 Jogging 1.446047149944e12 9.38908 -19.58108 8.58315 6.636980909090909 -18.389666363636362 5.719578181818182 88.1548232464 383.4186939664 73.67046392249999 23.350459976953342 22.55196135090203 2.752099090909091 1.191413636363638 2.8635718181818177 2.407844991735537 5.750263537190083 6.912224115702478 7.574049406182646 1.4194664529132273 8.200043557885122 9.657153846656074 41.139247568377066 86.3043109583581 3.1075961524393856 6.413988429080385 9.290011354048934
user_001 Jogging 1.446047149992e12 4.33079 -17.70339 2.18366 7.061987272727273 -19.392962727272728 3.0963790909090907 18.7557420241 313.41001749209994 4.768370995600001 18.355765593180795 21.769817840277774 2.7311972727272726 1.6895727272727292 0.9127190909090905 2.983601123966942 1.6176867768595058 2.8933422314049584 7.459438542552892 2.8546560007438084 0.8330561389099167 11.920819932043132 5.32959220910083 22.634681774097146 3.45265404175442 2.3085909575108428 4.75759201425439
user_001 Jogging 1.446047150009e12 5.86361 -14.56112 3.29495 7.765688181818183 -18.612621818181818 4.002131818181819 34.3819222321 212.02621565440003 10.856695502500001 16.03947734151584 20.98445602921786 1.9020781818181822 4.051501818181817 0.7071818181818186 2.7292931239669422 1.4770734710743818 1.7041457024793387 3.617901409748762 16.414666982730573 0.5001061239669428 10.436125994546856 4.233277587820513 7.70068862804275 3.230499341363012 2.057493034695504 2.775011464488525
user_001 Jogging 1.446047150024e12 7.1665 -11.72542 2.91174 7.898067272727272 -17.313215454545453 4.615257272727273 51.35872225 137.4854741764 8.4782298276 14.04715011146389 19.75562821218464 0.731567272727272 5.587795454545454 1.7035172727272734 2.720109256198347 1.9172815702479349 1.0900706611570252 0.5351906745256187 31.223458041838832 2.9019710984801677 10.436761381613074 7.754035861739667 1.7250466609229904 3.2305976817940474 2.784606949237121 1.3134103170460443
user_001 Jogging 1.446047150089e12 11.42005 0.920286 -10.76861 10.235605454545455 -6.9284110000000005 -5.013593999999999 130.4175420025 0.8469263217960001 115.96296133210001 15.72346748196453 16.668982547881402 1.1844445454545447 7.8486970000000005 5.755016000000001 2.9617473553719007 6.841284181818182 6.333937190082644 1.402908881257023 61.602044597809005 33.12020916025602 17.983586891344775 50.480642150793095 79.11948582376384 4.2407059425695595 7.104973057710571 8.894913480397875
user_001 Jogging 1.4460471503e12 11.80326 -19.58108 -4.86728 9.876788181818181 -16.619965454545454 5.089035181818182 139.3169466276 383.4186939664 23.6904145984 23.37575785279271 20.51629860347898 1.9264718181818186 2.9611145454545458 9.956315181818182 1.6841933057851242 8.302206694214878 7.953840752066115 3.711293666248762 8.768199351302481 99.12821199970321 4.3451937504936895 76.95784186172195 71.04635112082377 2.0845128328925417 8.772561875628005 8.428899757431202
user_001 Jogging 1.446047150316e12 13.02951 -19.58108 3.44823 10.841763636363636 -18.375732727272727 5.618552636363637 169.7681308401 383.4186939664 11.8902901329 23.771350717605426 22.540432916645994 2.1877463636363643 1.2053472727272734 2.1703226363636365 1.940401487603306 6.922042231404959 7.5085643553719015 4.786234151604135 1.4528620478710759 4.7103003459124055 5.182578915665215 62.486530982975154 68.06526032762473 2.2765278200947194 7.9048422490885395 8.25016729088718
user_001 Jogging 1.446047150381e12 5.02056 -16.13225 5.90073 9.730475454545456 -18.960987272727273 3.984714545454546 25.206022713599996 260.24949006249994 34.8186145329 17.89620427098998 21.991917768767674 4.709915454545456 2.828737272727274 1.9160154545454544 2.4594676033057854 1.1188903305785145 1.9137989752066118 22.18330358896613 8.001754558116536 3.6711152220570242 7.882300682133286 2.303614757833587 10.607043927891384 2.807543531654191 1.5177663712948666 3.2568457021927495
user_001 Jogging 1.446047150388e12 3.94759 -14.82936 5.70913 9.016323636363637 -18.52901272727273 4.946206363636364 15.583466808099999 219.90991800959998 32.5941653569 16.373379314442086 21.35533790164489 5.068733636363637 3.6996527272727295 0.7629236363636362 2.7451277685950415 1.1860301652892584 1.0780361074380165 25.692060676404143 13.687430302416546 0.5820524749223138 9.880552228511048 2.7508175715712295 1.6483021529113067 3.1433345715197176 1.6585588839625893 1.2838622016833843
user_001 Jogging 1.446047150446e12 -4.7128 -3.67815 -0.728685 1.3069736363636362 -10.878886363636362 2.3439079090909094 22.21048384 13.5287874225 0.530981829225 6.022478982256808 11.966450375373627 6.019773636363636 7.200736363636361 3.0725929090909094 5.286303041322314 5.421531652892561 2.5579606198347107 36.237674633058674 51.850604178595006 9.440827184995738 28.597294023410033 36.216624051849195 7.94891358854585 5.3476437823970695 6.018024929480535 2.819381774174234
user_001 Jogging 1.44604715051e12 -5.21096 0.498763 -1.34181 -6.489467272727273 -1.9398028181818185 -1.4532865454545456 27.1541041216 0.24876453016900002 1.8004540760999999 5.404009874886333 7.411970523117133 1.278507272727273 2.4385658181818184 0.11147654545454566 4.6402411735537195 5.203328504132231 2.136752809917356 1.6345808464165297 5.946603249604761 1.2427020186479384e-2 26.512593572034266 31.3340397920144 6.342812250172631 5.149038121050792 5.59768164439658 2.5184940441010837
user_001 Jogging 1.446047150519e12 -4.40624 0.230521 -1.03525 -6.698487272727272 -1.4172527272727273 -1.543862090909091 19.414950937600004 5.3139931441e-2 1.0717425625 4.5320893009230305 7.287043773994804 2.2922472727272716 1.6477737272727273 0.508612090909091 4.3330447272727275 4.609839090909092 1.8814949421487606 5.254397559325614 2.7151582562902563 0.25868625901891745 24.06618691699167 25.50364074727978 5.366435404843603 4.90573000857076 5.050112944012221 2.3165567993994025
user_001 Jogging 1.446047150535e12 -3.98471 1.15021 -0.767005 -6.6810681818181825 -0.518467 -1.5264437272727276 15.877913784100002 1.3229830441 0.5882966700250001 4.217723734222643 6.9728435823196095 2.6963581818181823 1.668677 0.7594387272727275 3.7319544793388433 3.533386834710744 1.4596547520661156 7.270347444657854 2.7844829303289997 0.5767471804816202 18.843668655735463 15.710387972942828 3.602534299062354 4.340929469103992 3.9636331784037266 1.8980343250485103
user_001 Jogging 1.446047150656e12 5.13552 -11.95534 4.78944 7.013215454545456 -3.5074520909090907 1.0270821818181823 26.373565670399998 142.93015451559998 22.938735513599998 13.865152566762472 12.758929470610324 1.8776954545454565 8.447887909090909 3.7623578181818176 6.062842892561983 3.6736822892561984 7.44934294214876 3.5257402200206687 71.36681012456437 14.155336352033848 49.57596519016131 20.885922032531145 78.13713376841855 7.041020181064766 4.5701118183837846 8.839521127777147
user_001 Jogging 1.446047150704e12 3.8919e-2 -19.38948 8.08499 6.577758090909092 -11.634841818181819 3.5004854545454545 1.514688561e-3 375.95193467039996 65.36706330009999 21.00762986771856 16.979426057591795 6.538839090909092 7.75463818181818 4.5845045454545446 3.814614214876033 6.555623876033058 8.284472793388431 42.756416656800845 60.134413330912366 21.01768192729338 18.63662567338302 46.999266380506135 106.19925324881555 4.317015829642395 6.855601095491637 10.305302191047847
user_001 Jogging 1.446047150729e12 6.28513 -19.58108 7.5485 6.539437181818181 -15.44248727272727 3.598028181818181 39.5028591169 383.4186939664 56.97985224999999 21.9066520795237 19.515162785692446 0.2543071818181817 4.13859272727273 3.9504718181818186 3.140049247933885 6.547072876033059 6.394109173553718 6.467214272430571e-2 17.127949762234735 15.606227586248764 14.839014316679823 46.59829215845338 70.57621021913586 3.8521441194067263 6.826294174620179 8.400964838584665
user_001 Jogging 1.446047150793e12 10.46204 -19.54276 6.24561 7.661177272727273 -19.535792727272725 5.656872090909091 109.4542809616 381.91946841760006 39.0076442721 23.030010717568068 22.099586635479316 2.800862727272727 6.967272727276708e-3 0.5887379090909093 2.9281772727272735 2.3704752066115735 2.3156854628099173 7.844832017025618 4.8542889256253815e-5 0.34661232560073574 12.87407932845424 9.62765954508025 7.460318108028584 3.588046728856 3.102847006392718 2.731358289940846
user_001 Jogging 1.446047150899e12 10.96021 1.95493 -8.08618 10.18335090909091 -6.249096636363637 -2.3416207272727267 120.1262032441 3.8217513049000003 65.38630699240001 13.759878689196356 14.293301046915387 0.77685909090909 8.204026636363636 5.744559272727274 1.2078809090909093 7.259007033057852 4.546814446280991 0.6035100471280977 67.30605305016404 32.99996123787691 2.1495073227730286 55.00847255568874 31.641875632767004 1.4661198186959443 7.4167696846867734 5.625111166258583
user_001 Jogging 1.446047150955e12 4.25415 3.71767 3.25663 9.152185454545453 2.581994272727273 -3.8883669090909097 18.0977922225 13.8210702289 10.6056389569 6.521081306677598 11.345821028162165 4.898035454545453 1.135675727272727 7.14499690909091 2.3831438842975206 6.168620760330578 5.639735181818182 23.990751313984283 1.2897593575164372 51.05098083091866 7.891078996077311 45.31626243044999 40.12753928982287 2.809106440859319 6.731735469435054 6.334630162039681
user_001 Jogging 1.446047150995e12 4.9056 -0.497565 -2.0699 5.626716363636364 3.031387181818182 0.48711390909090907 24.064911359999996 0.24757092922499999 4.28448601 5.347613327384937 6.885097826662445 0.721116363636364 3.5289521818181817 2.557013909090909 2.9680827272727273 3.1476498347107436 3.661964247933885 0.5200088099041328 12.453503501559306 6.538320131284372 11.189279831239894 14.854897650394623 17.366285791314564 3.345038091149321 3.854205190489295 4.167287582026775
user_001 Jogging 1.446047151012e12 3.56439 -1.34061 -12.8379 4.762767272727273 2.0176410909090907 -1.3174242727272727 12.7048760721 1.7972351721000002 164.81167641 13.390809820701659 7.32252464352399 1.198377272727273 3.358251090909091 11.520475727272727 2.8512215702479344 2.50602194214876 5.361042347107439 1.436108087789257 11.2778503895921 132.72136098268007 10.987531009836438 8.24752372582097 39.37473826934931 3.314744486357348 2.8718502269131254 6.274929343773467
user_001 Jogging 1.446047151093e12 3.60271 -19.58108 5.21096 4.881213636363636 -10.58974181818182 -0.8331956363636361 12.9795193441 383.4186939664 27.1541041216 20.580386717263114 13.800648451231167 1.2785036363636362 8.99133818181818 6.044155636363636 1.3541947107438017 7.364467082644628 5.066515809917355 1.634571548195041 80.84416229982146 36.531817356586316 2.329763991264012 62.92199581348555 32.83166793913865 1.5263564430577845 7.932338609356358 5.729892489317636
user_001 Jogging 1.446047151126e12 10.73029 -19.50444 -6.93658 6.086562727272726 -16.62344909090909 2.361324818181818 115.1391234841 380.42317971359995 48.116142096400004 23.316913288299975 18.38471454402584 4.643727272727274 2.880990909090908 9.297904818181818 1.5318631404958678 7.782823462809918 4.8175921652892555 21.564202983471084 8.300108618264456 86.45103400796867 3.852389123358829 67.63887646110612 27.84266451956603 1.9627503976203466 8.22428577209633 5.276614873151728
user_001 Jogging 1.446047151133e12 14.60064 -17.43514 -6.17017 6.818132727272726 -17.577972727272723 1.504343 213.1786884096 303.9841068196 38.0709978289 23.563399437646936 19.610273457596872 7.782507272727274 0.14283272727272234 7.674512999999999 2.0284438842975203 7.265657661157024 4.980373958677685 60.56741945005292 2.040118798016388e-2 58.89814978716899 8.869158837363564 64.54907492690951 30.04972946376538 2.978113301633026 8.034243892670268 5.481763353499071
user_001 Jogging 1.446047151142e12 15.67361 -17.93331 -1.49509 7.608924545454545 -18.25032 1.0235975454545456 245.6620504321 321.6036075561 2.2352941081 23.864219075769064 20.580314137387138 8.064685454545454 0.3170099999999998 2.5186875454545454 2.541492396694215 6.550239049586776 4.633907570247934 65.03915148075703 0.10049534009999987 6.343786951627843 14.2489020513701 58.46542353120962 26.984019767424993 3.774771787985348 7.646268601822043 5.194614496517041
user_001 Jogging 1.446047151215e12 1.91661 -12.91335 6.09233 7.103791818181819 -17.584940909090907 1.7342665454545454 3.6733938920999996 166.7546082225 37.11648482889999 14.406404372483093 19.79776161932016 5.18718181818182 4.671590909090908 4.358063454545454 4.890749752066115 1.391565537190083 2.648218975206611 26.90685521487605 21.82376162190081 18.99271707384466 28.641556203589325 4.338947391800674 10.980097076287576 5.351780657275607 2.083014016227609 3.3136229532473327
user_001 Jogging 1.446047151546e12 5.51872 -19.58108 1.76214 6.473250000000001 -17.111162727272724 2.2359154545454545 30.4562704384 383.4186939664 3.1051373796000004 20.420090640944764 20.381081270974065 0.954530000000001 2.469917272727276 0.47377545454545444 4.775471900826445 6.791562008264463 4.200666115702479 0.9111275209000019 6.100491334116545 0.22446318132975196 31.358268959488054 52.18630731844407 36.03881805361188 5.599845440678524 7.224009089033878 6.003233966256177
user_001 Jogging 1.446047151571e12 9.15915 -19.58108 2.79678 5.037978181818182 -19.107301818181814 4.193733636363636 83.8900287225 383.4186939664 7.8219783684 21.79749299936348 20.861238066323242 4.121171818181819 0.47377818181818654 1.3969536363636363 4.048650743801653 4.932551404958678 1.8906804958677683 16.984057154976036 0.2244657655669466 1.9514794621495868 24.858159910320957 34.60317561232702 6.249868547311647 4.985795815145357 5.882446396893645 2.4999737093240895
user_001 Jogging 1.446047151578e12 9.54236 -19.58108 2.60518 4.891664545454546 -19.56714545454545 4.1031581818181815 91.0566343696 383.4186939664 6.7869628323999995 21.93769110841886 21.159088532938316 4.650695454545454 1.3934545454549863e-2 1.4979781818181817 4.304542066115702 4.257987305785124 1.9438857024793388 21.628968210929752 1.9417155702491625e-4 2.2439386332033053 26.518021072216154 29.578972161291038 6.378130290521789 5.1495651342823265 5.43865536334957 2.5254960484074784
user_001 Jogging 1.446047151676e12 8.50771 -3.90807 -2.10822 5.870574545454546 -11.997141818181818 3.173018909090909 72.3811294441 15.2730111249 4.444591568400001 9.596808434964199 14.334378693583101 2.6371354545454535 8.089071818181818 5.281238909090909 1.8349409917355375 4.895182727272727 2.271032785123967 6.954483405620656 65.4330828797033 27.89148441489574 4.643321405980316 31.247187169837947 7.021995439934475 2.154836746944027 5.589918350909783 2.6499047982775674
user_001 Jogging 1.446047151862e12 3.10454 -14.3312 2.10702 4.99269 -3.4726144545454547 -3.4494249999999993 9.638168611600001 205.38329344000002 4.439533280399999 14.814215987759866 9.083787584658028 1.8881499999999996 10.858585545454545 5.556444999999999 1.6449227272727276 4.6769781404958675 2.5196400413223135 3.5651104224999983 117.90888004795438 30.87408103802499 3.093925017922089 31.651917087359298 9.060915545981608 1.7589556611586572 5.626003651559364 3.010135469705908
user_001 Jogging 1.44604715204e12 3.56439 -8.42987 2.91174 4.8951472727272725 -16.045159999999996 4.535131818181818 12.7048760721 71.06270821689999 8.4782298276 9.604468445291493 17.488520052165846 1.3307572727272725 7.615289999999996 1.623391818181818 3.4561126446281 2.750511818181819 2.702056834710744 1.7709149189165283 57.992641784099945 2.635400995339669 14.522404558036747 14.009495671867688 8.405549329122879 3.810827280005845 3.74292608421108 2.899232541401755
user_001 Jogging 1.446047152169e12 -4.82776 3.60271 -2.10822 -5.869378181818181 2.3694910000000005 -1.1014366363636368 23.307266617599996 12.9795193441 4.444591568400001 6.3821138763030545 6.586683677697039 1.0416181818181816 1.2332189999999996 1.0067833636363634 4.140811446280992 3.744305983471075 1.2370169504132227 1.0849684366942143 1.520829101960999 1.01361274129495 21.005204953242714 17.416097017278585 2.5625126737539987 4.5831435667282685 4.173259759142556 1.600785017968996
user_001 Jogging 1.446047152445e12 7.89458 -18.54643 3.17999 -1.3371281818181813 -2.117469090909091 -0.697331909090909 62.3243933764 343.9700657449 10.1123364001 20.40604801330723 11.0639760360617 9.231708181818181 16.42896090909091 3.877321909090909 5.280603446280992 5.684073314049588 2.931029776859504 85.22443595424875 269.91075655243725 15.033625186716371 47.08949045960139 74.9789026068423 15.588315749706124 6.862178259095387 8.659035893610922 3.9482041170266418
user_001 Jogging 1.446047152704e12 4.48408 -11.4955 2.79678 3.9545590909090915 -4.942721818181818 -0.791390909090909 20.106973446399998 132.14652025 7.8219783684 12.652093584257113 12.192673106227097 0.5295209090909081 6.552778181818182 3.588170909090909 6.058727438016527 6.943893842975206 3.8260147603305783 0.28039239316446174 42.9389019001124 12.87497047284628 54.759022243994444 85.08570595157579 20.00260483485849 7.399933935110127 9.224191344046144 4.472427174908328
user_001 Jogging 1.446047152769e12 11.11349 -18.16323 -2.8363 5.403763636363636 -6.9214436363636365 -0.85758 123.50965998010001 329.90292403289993 8.04459769 21.481554452669386 13.565349522260403 5.709726363636364 11.241786363636361 1.97872 6.483100909090908 7.853763603305786 3.914372636363637 32.60097514760414 126.37776064564045 3.9153328384000003 57.62411376316807 96.43633609191028 20.26639757095895 7.591054851808678 9.820200409966708 4.501821583643554
user_001 Jogging 1.446047153481e12 2.03158 -1.07237 -5.36544 4.700062727272727 -7.102593090909091 -0.19220027272727283 4.127317296399999 1.1499774169 28.787946393600006 5.8365435924783435 11.49641955233915 2.6684827272727274 6.03022309090909 5.173239727272728 4.461940330578512 7.525349793388429 2.330255355371901 7.120800065752893 36.36359052613318 26.76240927583281 31.50830018813525 63.92713021075553 8.885145880885544 5.613225470986824 7.995444341045439 2.9807961823790543
user_001 Jogging 1.446047153675e12 3.79431 -14.25456 3.86975 6.149267272727273 -9.903460272727271 -4.082727272727374e-3 14.396788376099998 203.1924807936 14.974965062499999 15.25005685996613 13.99042620816972 2.354957272727273 4.351099727272729 3.873832727272727 3.436792892561984 7.7863079669421476 3.2394917685950415 5.5458237563710755 18.932068836672816 15.006579998889254 17.24848748501127 69.499662545278 12.679372273498446 4.153129842060235 8.336645761052702 3.5608106202799448
user_001 Jogging 1.446047154387e12 9.04419 -18.69972 1.14901 5.361958363636363 -7.3150971818181825 0.22235518181818173 81.7973727561 349.6795280784 1.3202239801000002 20.803776695941533 12.021527729316709 3.682231636363637 11.384622818181818 0.9266548181818184 3.539086958677686 8.338626049586777 2.6770378925619838 13.558829823837229 129.6096367122661 0.8586891520595789 17.47642587546827 87.39473325913166 13.816889204735183 4.180481536314718 9.348515029625382 3.717107639648761
user_001 Jumping 1.446047227606e12 4.33079 -12.72175 -3.18118 4.33079 -12.72175 -3.18118 18.7557420241 161.8429230625 10.1199061924 13.810089473967938 13.810089473967938 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
user_001 Jumping 1.446047228189e12 7.85626 -19.2362 0.804128 2.5335707 -7.617479899999999 0.7811372000000001 61.720821187599995 370.03139044 0.646621840384 20.79420191947707 9.678680677882113 5.3226893 11.6187201 2.2990799999999867e-2 1.5381899021031746 5.749652194166667 1.5458001811904762 28.331021384334495 134.99465676214402 5.285768846399939e-4 4.741160399385161 58.53491368491284 5.359596330907423 2.1774205839444893 7.6508113089340295 2.3150801996707204
user_001 Jumping 1.4460472289e12 -2.10702 0.575403 1.07237 1.9479667272727275 -6.587010545454547 1.2813905454545456 4.439533280399999 0.331088612409 1.1499774169 2.433228166389046 8.318907723148978 4.054986727272727 7.162413545454546 0.20902054545454551 2.2773663388429752 6.5217368677685945 1.290223049586777 16.44291735835798 51.30016779611076 4.3689588422115726e-2 6.809434217026666 49.84400629186418 2.8670258503345463 2.6094892636350635 7.060028774152707 1.693229414560988
user_001 Jumping 1.446047229743e12 2.56806 -1.03405 0.267643 1.8504245454545454 -6.945829272727272 0.5149825454545455 6.5949321636 1.0692594024999997 7.163277544900001e-2 2.7813349926876842 8.172391978699084 0.7176354545454546 5.911779272727272 0.24733954545454545 1.3551465785123966 6.545490115702479 0.7524711818181818 0.5150006456206613 34.949134169447795 6.1176850745661156e-2 3.0300886047082014 52.47526121010706 0.9163994449650903 1.7407149694042967 7.243981033251472 0.9572875456022032
user_001 Jumping 1.446047229806e12 1.41845 -0.305964 0.727487 1.7424309090909091 -6.952796636363636 0.38608681818181817 2.0120004025 9.361396929600001e-2 0.529237335169 1.6232226301296442 8.01236384525454 0.32398090909090915 6.646832636363635 0.3414001818181818 1.3364614049586778 6.627197917355372 0.7062334793388431 0.10496362945537194 44.18038409582876 0.11655408414548761 3.014140832861232 53.488019562090564 0.8613111484622411 1.7361281153363168 7.313550407434857 0.9280685041861086
user_001 Jumping 1.446047230842e12 1.18853 1.41845 -2.22318 2.264980181818182 -5.869376909090908 0.3895704545454545 1.4126035609000003 2.0120004025 4.9425293124000005 2.892599743448789 7.889651174410864 1.0764501818181818 7.287826909090908 2.6127504545454547 2.5123547190082642 6.8102477603305775 1.0669505454545456 1.1587449939363965 53.11242105686954 6.82646493772748 8.933354789565023 51.82269572048727 1.797774661410906 2.988871825549738 7.198798213624776 1.3408111952884738
user_001 Jumping 1.446047231038e12 0.230521 0.728685 -0.690364 2.714373090909091 -5.855441727272727 0.19796945454545456 5.3139931441e-2 0.530981829225 0.476602452496 1.0299146630483518 7.593488780304369 2.483852090909091 6.584126727272727 0.8883334545454545 2.2102257685950413 6.819115685950414 1.1448584710743803 6.169521209513464 43.35072476078707 0.7891363264646611 6.836162861352534 51.7026766598987 1.7857949604733845 2.6146056798975508 7.190457333153344 1.3363363949520288
user_001 Jumping 1.446047231555e12 -0.919089 -0.382604 0.114362 2.867653454545455 -6.116717181818182 0.5776896363636365 0.8447245899210001 0.146385820816 1.3078667044000002e-2 1.0020923499263927 8.397198505817867 3.786742454545455 5.7341131818181825 0.46332763636363644 3.6160431239669424 7.249506231404959 1.7985207438016528 14.339418417056937 32.88005398190104 0.2146724986183141 15.941718766454512 64.06415040944202 4.433685351168226 3.99270819951252 8.004008396387526 2.1056318175712074
user_001 Jumping 1.446047231749e12 2.29982 -1.49389 -1.26517 3.226471181818182 -6.371024272727272 0.598591 5.2891720324 2.2317073320999996 1.6006551288999997 3.020187824192396 8.506630980416517 0.926651181818182 4.877134272727272 1.8637609999999998 3.3744030247933883 7.032252669421488 1.7465819752066116 0.8586824127650333 23.786438714210973 3.4736050651209993 15.020525370126592 61.25263121234784 4.396616733337844 3.875632254242731 7.826406021434605 2.096811086707108
user_001 Jumping 1.446047232138e12 -1.68549 3.67935 -0.881966 2.258014090909091 -5.886794272727272 -0.927253090909091 2.8408765400999996 13.5376164225 0.7778640251560001 4.142023296380164 8.319049063739739 3.943504090909091 9.566144272727271 4.5287090909091e-2 2.489552314049587 7.391703132231405 1.3665452975206611 15.551224515016735 91.51111624663278 2.0509206030082726e-3 8.76062525277227 62.356581009384314 2.8936035211928766 2.959835342172309 7.896618327447789 1.701059528997406
user_001 Jumping 1.44604723272e12 -3.7722e-2 -1.68549 2.6435 2.163956181818182 -6.670619181818182 0.14919809090909086 1.422949284e-3 2.8408765400999996 6.98809225 3.135345553425332 8.126728546908634 2.201678181818182 4.985129181818182 2.4943019090909093 1.6430228429752065 6.649998520661156 1.3282255289256197 4.847386816294216 24.85151295941522 6.221542013694555 3.9847162270974086 50.549925642431326 2.8597598656943437 1.996175399882838 7.109847089947246 1.6910824538426101
user_001 Jumping 1.446047233044e12 2.37646 -3.29495 -1.45677 2.1987926363636365 -6.611396545454545 -0.2723257272727273 5.647562131599999 10.856695502500001 2.1221788328999995 4.315835546797398 8.230510968189018 0.17766736363636326 3.3164465454545446 1.1844442727272726 1.4631399917355374 6.803913528925619 1.6708914710743803 3.1565692101495735e-2 10.998817688857383 1.4029082351964377 2.7418291416220666 52.41877920656386 3.830057240371654 1.6558469559781384 7.2400814364593895 1.957053203255255
user_001 Jumping 1.446047234792e12 5.99e-4 -1.11069 -0.230521 3.3309803636363635 -6.2699974545454555 -0.9551216363636363 3.5880100000000004e-7 1.2336322760999998 5.3139931441e-2 1.1343599809328606 8.289652387457776 3.3303813636363637 5.159307454545456 0.7246006363636364 2.579495214876033 6.605979950413223 1.3551450247933883 11.091440027256406 26.618453410528307 0.5250460822185867 11.11725107929375 53.90737983996103 2.5507655785709034 3.3342542013610403 7.342164520082687 1.5971116362267552
user_001 Jumping 1.446047236669e12 0.11556 -0.114362 -1.11189 2.7248254545454547 -5.9285986363636365 0.25719245454545453 1.3354113599999998e-2 1.3078667044000002e-2 1.2362993721000002 1.1237135545787458 7.6763875816918326 2.6092654545454548 5.814236636363637 1.3690824545454545 2.8306369256198347 6.579058876033057 1.2154832396694213 6.808266212284298 33.805347663633135 1.8743867673442065 9.500612024374687 54.4232190659533 2.0968215239484818 3.082306283349318 7.37720943622677 1.4480405809052734
user_001 Jumping 1.44604723751e12 1.41845 -0.459245 -1.38013 2.7457267272727273 -5.9146635454545455 4.468827272727274e-2 2.0120004025 0.210905970025 1.9047588169000003 2.0316656194918004 7.9543184777753995 1.3272767272727273 5.455418545454545 1.424818272727273 2.351473256198347 6.676601545454546 0.9963275289256198 1.7616635107598018 29.76159150608939 2.0301071102975294 9.396080794295077 54.67752169176086 1.3210375907394523 3.065302724739447 7.394425041324096 1.1493639940155826
user_001 Jumping 1.446047237964e12 2.6447 -3.7722e-2 1.18733 3.101061272727273 -5.656873181818182 0.2188711818181818 6.994438089999999 1.422949284e-3 1.4097525289 2.89924362001264 7.663649011187349 0.456361272727273 5.619151181818182 0.9684588181818182 2.099383173553719 6.700038338842975 1.0824689586776859 0.20826561124525644 31.574860004128674 0.9379124825141241 9.368198813922534 55.118015671780014 1.3014943944823985 3.060751347940981 7.424150838431289 1.1408305722071084
user_001 Jumping 1.446047239453e12 1.26517 -0.305964 -5.99e-4 3.1811840909090914 -5.817121727272728 4.468927272727272e-2 1.6006551288999997 9.361396929600001e-2 3.5880100000000004e-7 1.3016410630419586 7.57792755101516 1.9160140909090915 5.511157727272727 4.5288272727272726e-2 2.5278747272727267 6.920141305785125 1.1382085454545456 3.6711099965621923 30.372859494877893 2.0510276466198345e-3 9.38379122850827 58.07419735812502 1.5827917125439923 3.063297443688463 7.6206428441519956 1.2580905025251532
user_001 Jumping 1.446047239777e12 1.80165 -6.01569 -0.422122 3.264792363636364 -6.590495636363636 5.165563636363639e-2 3.2459427224999997 36.188526176100005 0.178186982884 6.293858584484084 8.267906869265873 1.463142363636364 0.574805636363636 0.4737776363636364 2.098750636363637 6.206623462809918 0.98239347107438 2.1407855762674064 0.33040151959540454 0.22446524871831408 6.578081373559175 50.15157456756155 1.2001631730020994 2.564777061180791 7.0817776417762195 1.0955195904236945
user_001 Jumping 1.4460472401e12 0.996927 3.8919e-2 -0.575403 2.8502368181818176 -5.782284454545455 -0.1294945454545454 0.993863443329 1.514688561e-3 0.331088612409 1.1517233801130375 7.488380834527844 1.8533098181818177 5.821203454545455 0.4459084545454546 2.339439314049587 6.414693702479339 1.1030548595041323 3.434757282169122 33.88640965921194 0.19883434983511572 7.295192824921782 51.8848540825245 1.7815078835544063 2.700961463057513 7.20311419335585 1.3347313900386124
user_001 Jumping 1.446047240878e12 4.40743 -11.61046 0.459245 2.8363007272727274 -7.05730681818182 -9.814018181818178e-2 19.425439204899998 134.8027814116 0.210905970025 12.427353965608487 9.226881520769744 1.5711292727272723 4.55315318181818 0.5573851818181818 2.7457610330578515 7.554485462809916 1.3038408595041322 2.4684471916205277 20.731203897101018 0.3106782409104875 9.850639666806897 63.88737605553916 2.4539795641499778 3.138572871036595 7.992957904026466 1.5665182935893145
user_001 Jumping 1.446047241266e12 2.22318 -1.80046 1.80046 2.5785103636363633 -6.357090454545454 1.009665 4.9425293124000005 3.2416562115999996 3.2416562115999996 3.3802132677687657 8.380790617311566 0.35533036363636317 4.556630454545454 0.7907949999999999 2.8281013636363634 7.1047753801652895 2.178558561983471 0.12625966732195007 20.76288109929111 0.6253567320249999 10.393818910917538 58.5980634373097 6.668674357389767 3.2239446197038713 7.654937193557482 2.582377655841563
user_001 Jumping 1.446047241913e12 1.07357 -1.03405 -0.613724 2.7875318181818183 -5.768350909090909 0.8947032727272725 1.1525525448999998 1.0692594024999997 0.37665714817600005 1.6119767664504348 7.966962402686918 1.7139618181818184 4.734300909090909 1.5084272727272725 3.4725796446280985 6.402026396694215 2.2985853223140498 2.9376651141851244 22.413605097819012 2.2753528371074374 16.3891356554726 48.56199855497939 9.77557814309428 4.048349744707416 6.968643953810482 3.126592097331259
user_001 Jumping 1.446047242172e12 6.93658 -10.84405 -0.422122 3.5504547272727276 -6.531273454545455 1.068886727272727 48.116142096400004 117.59342040249999 0.178186982884 12.879741825121496 8.868355706458432 3.3861252727272726 4.312776545454544 1.4910087272727268 3.5162844710743797 6.2994165371900825 2.3676246446280995 11.465844362602347 18.600041531022832 2.223107024803437 16.457890970833663 47.36959226026294 9.601871044209373 4.056832627904886 6.882557101852693 3.0986886007163372
user_001 Jumping 1.446047242884e12 10.50036 -19.58108 1.8771 5.0588799999999985 -7.639077636363638 -0.2862584545454545 110.25756012960001 383.4186939664 3.52350441 22.297976556315596 10.558958547804354 5.441480000000002 11.942002363636362 2.1633584545454543 4.1826142231404955 7.356550206611572 1.5752493140495865 29.60970459040002 142.61142045309646 4.680119802853296 28.286595726482048 63.57031171260442 3.541155966070285 5.318514428530024 7.973099253903993 1.881795941665909
user_001 Jumping 1.446047243143e12 0.307161 1.53341 -2.49142 3.6340609090909086 -5.660356454545454 -0.3315469090909091 9.434787992100001e-2 2.3513462280999997 6.207173616400001 2.941575721347489 8.185633262013813 3.3268999090909084 7.193766454545454 2.159873090909091 3.1970538347107436 6.646516429752068 1.4789741074380165 11.068263005109095 51.75027580254347 4.665051768833191 14.673029832308737 51.88884227807641 2.987737094353247 3.8305391046572983 7.2033910263206185 1.7285071866652006
user_001 Jumping 1.446047243531e12 11.57333 -19.58108 0.344284 4.5014933636363645 -7.2245218181818185 4.817318181818176e-2 133.9419672889 383.4186939664 0.11853147265599999 22.748168997261207 9.614007130330195 7.071836636363636 12.356558181818182 0.2961108181818182 3.602741462809917 7.240955603305786 1.341211165289256 50.01087341141494 152.68453010065784 8.768161664430581e-2 18.025288293019972 62.05824709530112 2.6538719664479 4.245619895023573 7.877705699967543 1.6290708905532318
user_001 Jumping 1.446047244373e12 -0.535886 -1.18733 1.64717 4.111323636363637 -5.952984272727273 -0.17478236363636365 0.287173804996 1.4097525289 2.7131690089 2.10002270054302 8.42056546855258 4.647209636363637 4.765654272727272 1.8219523636363637 3.491582256198347 6.728223553719008 0.8411461652892562 21.596557404311042 22.711460647163708 3.3195104153601327 18.261239277957863 53.18916722596664 1.0814781705921834 4.273317128175472 7.293090375551824 1.0399414265198705
user_001 Jumping 1.446047244502e12 -1.72382 0.690364 0.191003 3.6027080000000002 -5.8658920909090915 1.6818909090909072e-2 2.9715553923999996 0.476602452496 3.6482146009e-2 1.8667190444480388 8.710287378942498 5.326528 6.556256090909091 0.17418409090909093 4.041685214876034 6.887205876033058 0.6983162396694215 28.371900534783997 42.984493929582555 3.034009752582645e-2 24.406443491662195 55.8220753644146 0.7729212899290271 4.9402877944166566 7.471417225962863 0.8791594223626492
user_001 Standing 1.446047263599e12 1.22685 -9.27292 0.191003 1.1188554545454545 -9.346076363636364 0.40002272727272725 1.5051609225 85.98704532639998 3.6482146009e-2 9.355676800473015 9.427912904892985 0.10799454545454545 7.315636363636457e-2 0.20901972727272725 0.213428500603437 8.054413590450014e-2 0.1583984693755739 1.1662821847933885e-2 5.351853540496005e-3 4.368924638916528e-2 7.091546002166214e-2 9.146781793338572e-3 3.574611894166528e-2 0.26629956819653716 9.56388090334597e-2 0.18906644054846244
user_001 Standing 1.446047265606e12 1.22685 -9.2346 -0.1922 0.9516395454545455 -9.36001090909091 -0.2200696363636364 1.5051609225 85.27783716 3.694084e-2 9.317721766746418 9.41792726022171 0.27521045454545445 0.12541090909090968 2.7869636363636402e-2 0.2001527107438017 0.10862611570247971 0.20300272727272725 7.574079429111565e-2 1.5727896119008412e-2 7.767166310413244e-4 6.74780467919369e-2 1.5294319858151866e-2 5.381838598250938e-2 0.25976536873097017 0.12367020602453878 0.23198790050886142
user_001 Standing 1.446047265736e12 1.03525 -9.46452 -0.613724 0.9934438181818183 -9.373945454545453 -0.27580827272727276 1.0717425625 89.5771388304 0.37665714817600005 9.540730503534622 9.43637041659947 4.180618181818174e-2 9.057454545454746e-2 0.3379157272727273 0.18526814049586776 0.12287735537190142 0.2039529008264463 1.7477568382148697e-3 8.203748284297884e-3 0.11418703873825621 5.9142881348738546e-2 1.964663117896333e-2 5.5500906570311793e-2 0.24319309478013257 0.1401664409870042 0.23558630386826776
user_001 Standing 1.446047265929e12 0.958607 -9.34956 -0.230521 0.9795095454545454 -9.384396363636363 -0.32806318181818184 0.918927380449 87.41427219360001 5.3139931441e-2 9.401400933131722 9.44541709001559 2.0902545454545396e-2 3.483636363636222e-2 9.754218181818183e-2 0.13142985950413222 9.595834710743874e-2 0.1992023388429752 4.369164064793364e-4 1.2135722314048601e-3 9.514477233851243e-3 2.979612839872803e-2 1.4155768455597456e-2 5.6693495851969186e-2 0.17261555086007757 0.11897801669046873 0.23810396017699745
user_001 Standing 1.446047269426e12 0.690364 -9.34956 3.7722e-2 0.6555278181818183 -9.401814545454544 0.13178036363636367 0.476602452496 87.41427219360001 1.422949284e-3 9.375089204662535 9.427105421840285 3.483618181818171e-2 5.225454545454333e-2 9.405836363636366e-2 0.11147730578512394 4.3703801652892824e-2 0.10831033057851239 1.213559563669414e-3 2.7305375206609353e-3 8.846975769950418e-3 1.8563579805789626e-2 3.104538417430562e-3 2.244263762957626e-2 0.1362482286335849 5.571838491405294e-2 0.1498086700747866
user_001 Standing 1.446047269555e12 0.652044 -9.4262 0.267643 0.6311421818181817 -9.401814545454544 0.14919863636363637 0.42516137793599995 88.85324643999999 7.163277544900001e-2 9.452515040632573 9.425761237002126 2.0901818181818244e-2 2.4385454545456042e-2 0.11844436363636365 0.10736015702479335 4.5287272727273245e-2 8.297457851239672e-2 4.368860033057877e-4 5.946503933885027e-4 1.4029067277223145e-2 1.902580785260781e-2 3.1630105340346294e-3 1.5928957561460556e-2 0.13793407067366573 5.6240648414066396e-2 0.1262099740965846
user_001 Standing 1.446047271885e12 0.652044 -9.57948 -5.99e-4 0.7495870909090908 -9.520258181818182 -0.3385142727272727 0.42516137793599995 91.7664370704 3.5880100000000004e-7 9.60164563015825 9.56080406607656 9.754309090909086e-2 5.9221818181818264e-2 0.3379152727272727 0.2087035702479339 0.22263603305785085 0.15169771074380167 9.514654584099164e-3 3.5072237487603405e-3 0.11418673154234707 6.712845657103984e-2 6.522730094305014e-2 2.9760565016948907e-2 0.259091598804438 0.2553963604733829 0.1725125068421096
user_001 Standing 1.446047274022e12 0.460442 -9.69444 -0.383802 0.540567 -9.440133636363637 -0.1643308181818182 0.21200683536400003 93.9821669136 0.147303975204 9.712954119327858 9.464250160317123 8.0125e-2 0.2543063636363634 0.2194711818181818 0.18875167768595047 0.20870247933884284 0.2182040743801653 6.420015625e-3 6.467172658595029e-2 4.816759964866941e-2 5.836297226791512e-2 5.4720719320510834e-2 6.432368563568823e-2 0.2415842964017221 0.233924601785513 0.2536211458764593
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user_001 Standing 1.446047274733e12 0.11556 -9.65612 0.152682 0.1678146363636364 -9.419230909090908 9.852181818181826e-3 1.3354113599999998e-2 93.24065345439999 2.3311793124000002e-2 9.65801839722435 9.439390027438327 5.225463636363639e-2 0.2368890909090915 0.1428298181818182 0.29262790082644635 0.24765694214876033 0.31257953719008263 2.730547021495871e-3 5.6116441391735813e-2 2.0400356961851242e-2 0.15356138736965594 9.768998214567995e-2 0.19560538992085943 0.39186909468552883 0.3125539667732277 0.44227298122410713
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user_002 Jogging 1.446034901543e12 -6.7821 -8.35323 -0.15388 -1.9293514545454549 -4.0265189090909095 -1.0596333636363637 45.996880409999996 69.7764514329 2.3679054399999996e-2 10.760901955565807 6.529144512249854 4.852748545454545 4.3267110909090905 0.9057533636363637 3.989429066115703 2.2393638842975205 1.7814196280991736 23.549168445411198 18.720428864195732 0.820389155738587 21.84543006964122 6.035619134752426 4.882249051245194 4.673909505931968 2.456749709423495 2.2095811936304113
user_002 Jogging 1.446034901568e12 -13.90968 -14.25456 2.37526 -5.576748727272728 -7.1200127272727265 0.685683 193.4791977024 203.1924807936 5.6418600676 20.05775507287892 9.777926846037717 8.332931272727272 7.134547272727273 1.6895769999999999 5.3965136033057854 3.848816256198347 2.33152167768595 69.43774359599615 50.90176478678017 2.8546704389289994 32.19524319849596 19.23855199524021 7.38217409989887 5.674085230105022 4.386177378451562 2.7170156605913904
user_002 Jogging 1.446034901754e12 -1.80046 -4.75112 -0.345482 -7.733138636363637 -10.610643636363637 0.5846561818181819 3.2416562115999996 22.573141254400003 0.119357812324 5.092558814419722 13.50282014837676 5.932678636363637 5.859523636363637 0.930138181818182 4.5943209504132225 3.3978410743801657 0.9003685454545457 35.1966758023655 34.334017245104135 0.8651570372760333 29.45408911006125 14.127866162308719 1.2462307041419791 5.427162159919423 3.758705383813517 1.1163470357115564
user_002 Jogging 1.446034901778e12 -2.87342 0.958607 -3.48775 -4.932271363636365 -6.635782363636365 -0.19916863636363624 8.2565424964 0.918927380449 12.1644000625 4.619509707679918 9.170021680842996 2.058851363636365 7.594389363636365 3.288581363636364 4.947438099173554 5.119720438016529 1.120473223140496 4.238868937547319 57.674749806513155 10.814767385256406 30.827081428873772 29.06976515844823 2.2164938726372085 5.5522141014980475 5.391638448416978 1.488789398349279
user_002 Jogging 1.446034901818e12 -4.9044 4.25415 -4.02423 -2.5459604545454546 -0.9399914545454545 -3.32749890909091 24.05313936 18.0977922225 16.1944270929 7.6384133611241545 6.456276805127437 2.3584395454545453 5.194141454545455 0.6967310909090902 3.4811313636363637 5.85255605785124 2.658035719008265 5.562237089563842 26.97910544982757 0.48543421303937095 19.643839108268764 36.150759753165694 9.796203638719605 4.432137081394117 6.012550187163987 3.1298887582020556
user_002 Jogging 1.44603490198e12 -19.58108 -9.00468 -3.56439 -8.276589090909091 -8.83745909090909 -2.00719 383.4186939664 81.0842619024 12.7048760721 21.845087135118046 13.987212825794312 11.304490909090909 0.1672209090909096 1.5572 6.14391758677686 4.873330545454544 3.3848551074380167 127.791514713719 2.796283243719025e-2 2.42487184 63.11184264424193 39.816429316796594 13.797553939075534 7.944296233414382 6.310026094779371 3.7145058808777693
user_002 Jogging 1.446034902086e12 -12.18526 -5.82409 -3.90927 -15.679373636363636 -11.188933636363636 -7.281458181818183 148.4805612676 33.9200243281 15.282391932899998 14.059977863730795 20.738969766811962 3.494113636363636 5.364843636363636 3.3721881818181836 1.291173578512396 2.5475080991735535 2.0585292561983475 12.208830103822311 28.7815472426314 11.371653133594227 3.1528208578917405 9.549293706104132 6.302081652987829 1.7756184437800089 3.0901931502907924 2.5103947205544848
user_002 Jogging 1.446034902207e12 1.57173 1.22685 -1.15021 -1.2779061818181818 1.5125097272727273 -0.7844235454545454 2.4703351929000004 1.5051609225 1.3229830441 2.3018425574960597 3.8283394853389723 2.849636181818182 0.28565972727272726 0.36578645454545455 5.201743809917356 3.6169951900826445 1.362746347107438 8.120426368727308 8.160147978552892e-2 0.13379973032893389 28.055339392748365 15.483652908929882 3.2315638527796566 5.296729122085475 3.9349273066893984 1.7976550983933643
user_002 Jogging 1.446034902215e12 0.460442 0.268841 -1.57173 -0.6752323636363635 1.7180461818181814 -0.8889333636363635 0.21200683536400003 7.2275483281e-2 2.4703351929000004 1.6597040433598396 3.3886435757782847 1.1356743636363635 1.4492051818181815 0.6827966363636365 4.750450900826447 3.344636074380165 1.1093888181818181 1.2897562602208592 2.1001956590086683 0.4662112466294961 24.78997763030444 13.878270058378378 2.179490103587765 4.978953467376899 3.7253550244746307 1.4763096232117994
user_002 Jogging 1.446034902231e12 -1.57053 -0.344284 -1.11189 -0.11784572727272725 1.8573923636363632 -1.1467244545454547 2.4665644809 0.11853147265599999 1.2362993721000002 1.9548389513348663 2.9538514725909635 1.4526842727272726 2.201676363636363 3.483445454545464e-2 3.776608099173554 2.949714570247934 0.648277909090909 2.110291596229165 4.847378810195039 1.2134392234793455e-3 17.801429361908134 11.44855536925793 0.6513529155226738 4.219174014177199 3.383571392664551 0.8070643812749227
user_002 Jogging 1.446034902514e12 -2.91174 -7.28026 -1.53341 -13.742459090909092 -11.533813636363638 -2.3033 8.4782298276 53.0021856676 2.3513462280999997 7.989478188423822 18.360166618428106 10.830719090909092 4.2535536363636375 0.7698900000000002 6.058093305785124 2.7144082644628105 0.724285438016529 117.30447602618267 18.092718537422325 0.5927306121000003 46.810740975525555 8.797815719086705 0.7294053996474156 6.841837543783509 2.966111211516976 0.8540523401100284
user_002 Jogging 1.446034902531e12 -2.33694 -4.55952 -1.61005 -10.610644545454544 -9.711857272727274 -2.2823972727272728 5.461288563599999 20.7892226304 2.5922610025 5.370546731618672 14.921223269515052 8.273704545454544 5.152337272727274 0.6723472727272728 6.659500743801653 3.3094812396694224 0.8186608925619836 68.45418690547518 26.546579371934723 0.4520508551438017 55.78962539186213 12.58307267179482 0.8407906514539085 7.469245302697062 3.5472627012662623 0.916946373270492
user_002 Jogging 1.446034902627e12 -2.68182 -0.535886 -1.68669 -4.650093636363636 2.359038545454545 -3.0940923636363635 7.192158512400001 0.287173804996 2.8449231561 3.213137948096222 6.405242851026029 1.9682736363636355 2.894924545454545 1.4074023636363635 0.9624421487603303 4.815373719008264 1.4479379008264461 3.8741011076041287 8.380588123875205 1.9807814131692227 1.8753445041277237 29.04896108408565 3.2992674363277446 1.3694321831064595 5.389708812550605 1.8163885697525584
user_002 Jogging 1.446034902684e12 -0.191003 -8.65979 1.45557 -1.7203319090909088 -2.8560078181818183 -1.2163973636363639 3.6482146009e-2 74.99196284409999 2.1186840249000003 8.783343840190307 5.8018233301148125 1.5293289090909088 5.803782181818181 2.671967363636364 1.8909967272727266 4.315626595041322 2.0445943223140493 2.338846912181189 33.68388761399021 7.139409592337862 4.752487980665275 22.310358190105372 4.801100736618481 2.180020178958276 4.723384188281255 2.1911414232354973
user_002 Jogging 1.446034902701e12 -2.41358 -8.46819 0.727487 -1.2361019090909091 -5.099487818181818 -0.15039581818181824 5.8253684164 71.7102418761 0.529237335169 8.8354313775655 6.140365980333311 1.177478090909091 3.3687021818181817 0.8778828181818182 2.0145087107438013 4.656392776859504 2.0490282396694215 1.3864546545709175 11.348154389786577 0.7706782424588513 4.8853431088144275 24.57087881120827 4.879751059280171 2.210281228444568 4.956902138554711 2.2090158576343835
user_002 Jogging 1.446034902805e12 -17.62674 -9.08132 -6.40009 -15.128957272727273 -12.470921818181818 -6.333900909090909 310.7019630276001 82.47037294239999 40.961152008099994 20.835870223681564 20.78196857637037 2.497782727272728 3.389601818181818 6.618909090909053e-2 6.036874694214876 2.4832193388429755 3.284779181818182 6.238918552661988 11.489400485821488 4.3809957553718505e-3 41.12672443825338 7.965350005252444 13.045420306964319 6.413012118985383 2.8222951662171063 3.6118444466732393
user_002 Jogging 1.446034902968e12 4.63736 -0.919089 -3.2195 -0.7205193636363639 0.31064381818181813 -0.2026514545454545 21.505107769600002 0.8447245899210001 10.36518025 5.719703891769311 4.442509944887756 5.357879363636364 1.2297328181818181 3.0168485454545455 6.339320231404958 2.474667537190083 3.0231858347107434 28.70687127528041 1.5122428041133966 9.101375146211208 40.40514044965991 6.740364931990786 10.65622385603228 6.3565037913667535 2.5962212794734554 3.2643872098806357
user_002 Jogging 1.446034902976e12 5.67201 -2.8351 -2.52974 0.4534760909090909 0.2374874545454545 -0.5266323636363637 32.171697440100004 8.03779201 6.3995844675999995 6.827083851667563 4.372978499695182 5.218533909090909 3.0725874545454546 2.0031076363636364 6.274081082644628 2.4797344132231407 2.742275867768595 27.233096160331645 9.440793665830116 4.012440202858314 39.67741741780719 6.7712193658965285 8.662823551405499 6.2990013032072945 2.6021566758933883 2.94326749572741
user_002 Jogging 1.446034903e12 6.20849 -3.71647 -3.0279 3.466846090909091 -0.5637553636363637 -1.5125087272727271 38.545348080100005 13.812149260900002 9.16817841 7.843830425946242 5.121713069249923 2.7416439090909095 3.1527146363636365 1.5153912727272727 5.613451404958678 2.6273143719008263 1.9939214214876033 7.516611324255283 9.939609578341496 2.2964107094579833 33.31595687994492 7.729724814435821 4.668799177641327 5.771997650722401 2.7802382657671303 2.1607404234755565
user_002 Jogging 1.446034903122e12 -15.05928 -10.46085 0.229323 -10.676833636363638 -10.809214545454546 0.23977427272727272 226.78191411839998 109.42938272250001 5.2589038329e-2 18.337499444559747 15.370729188349905 4.382446363636362 0.34836454545454565 1.0451272727272726e-2 7.050937512396694 3.9726451900826447 1.4612389256198348 19.20583613014957 0.1213578565297522 1.0922910161983468e-4 50.68204593155306 22.592195796465415 2.9680132535840995 7.119132386151635 4.7531248454532955 1.722792283934456
user_002 Jogging 1.446034903162e12 -15.82569 -12.79839 -0.345482 -13.836517272727274 -12.927282727272729 0.260676 250.4524639761 163.7987865921 0.119357812324 20.35609511621824 19.101228338167484 1.9891727272727255 0.1288927272727296 0.606158 4.112941603305784 2.917411074380166 1.1961640578512398 3.956808138925613 1.6613335143802255e-2 0.36742752096399994 25.41021847834294 18.272074295056942 2.3195890725029122 5.040854935260778 4.274584692699039 1.5230197216395172
user_002 Jogging 1.446034903307e12 -1.53221 -2.49022 -1.30349 -5.392114545454546 -6.336188181818182 -2.083830909090909 2.3476674841 6.2011956484 1.6990861801000001 3.2012418391305584 8.739578917812501 3.8599045454545458 3.845968181818182 0.780340909090909 5.506407685950413 3.3297501652892563 1.055867 14.898863100020664 14.791471255557852 0.6089319344008264 31.50156618148407 11.305911970917434 1.225309888233371 5.612625604962803 3.362426500448364 1.106937165440465
user_002 Jogging 1.446034903364e12 -3.06503 3.90927 -2.52974 -2.817686363636364 0.32109581818181826 -3.007001818181818 9.3944089009 15.282391932899998 6.3995844675999995 5.574619745005035 5.520307117261362 0.24734363636363632 3.5881741818181814 0.47726181818181823 2.2561485950413216 4.613006 1.049850388429752 6.117887444958676e-2 12.874993959066575 0.22777884309421492 10.156513458621633 22.844478304031163 1.672854066725234 3.186928530516747 4.779589763152394 1.2933885984982372
user_002 Jogging 1.446034903389e12 -0.114362 -2.29862 1.18733 -2.5982147272727274 1.533411636363636 -2.2580138181818183 1.3078667044000002e-2 5.2836539044 1.4097525289 2.5896882245444144 4.741289185702595 2.4838527272727275 3.832031636363636 3.4453438181818186 1.128391652892562 4.422671603305786 1.6686763140495868 6.169524370780167 14.684466462091768 11.870394025483671 2.6154585313649137 22.066950396758074 4.132894945850269 1.6172379328240214 4.697547274563405 2.0329522733823016
user_002 Jogging 1.446034903453e12 -4.06135 -6.59049 0.842448 -0.9260550909090909 -2.514606 1.138559636363636 16.4945638225 43.4345584401 0.7097186327039999 7.787094509205857 3.6863808338969126 3.1352949090909092 4.075884 0.29611163636363613 1.7944037190082645 3.1096454049586773 2.334055776859504 9.830074166971373 16.612830381456003 8.768210118995028e-2 4.132053315964243 10.482384637933924 6.663167319451804 2.032745265881646 3.2376510988576155 2.581311162849571
user_002 Jogging 1.446034903559e12 -19.58108 -10.42253 -8.81427 -15.08018545454545 -16.330821818181818 -7.13166 383.4186939664 108.6291316009 77.69135563290001 23.86920989895141 23.72028927423204 4.50089454545455 5.908291818181818 1.6826100000000004 5.996020479338842 5.813287438016529 3.578356950413223 20.258051709302517 34.90791220879421 2.8311764121000014 37.15895341889142 43.90340861610187 14.47403434508205 6.095814418015974 6.625964730973284 3.80447556768105
user_002 Jogging 1.446034903656e12 -3.02671 -2.10702 1.83878 -12.244483636363638 -4.859112727272729 -3.811728818181818 9.1609734241 4.439533280399999 3.3811118884000004 4.120875949710206 13.973353179277263 9.217773636363638 2.752092727272729 5.650508818181818 5.437367190082646 4.621873553719009 3.1761519338842983 84.96735081124054 7.574014379507447 31.928249904350483 40.0247632765042 23.596950291099475 14.544418632169284 6.326512726337015 4.857669224134089 3.81371454518679
user_002 Jogging 1.44603490385e12 -13.52647 -11.72542 2.91174 -8.245234727272727 -7.551986 -0.9133200000000002 182.9653906609 137.4854741764 8.4782298276 18.13640247306229 12.780088083552192 5.2812352727272724 4.173433999999999 3.82506 6.257928099173554 4.886315537190083 2.9636499669421483 27.891446005898707 17.417551352355996 14.631084003600002 44.13147140172497 40.37989817122545 16.726569752810427 6.643152218768209 6.354517933818855 4.089812923938016
user_002 Jogging 1.446034903963e12 -10.38421 -11.84038 0.842448 -14.96870909090909 -12.693877272727274 -1.4532909090909076e-2 107.83181732409999 140.19459854439998 0.7097186327039999 15.771370723599263 19.95964069919205 4.584499090909091 0.8534972727272745 0.8569809090909091 3.128014958677686 1.8362072727272731 2.8122667933884298 21.017631914546282 0.7284575945528956 0.734416278546281 11.367615322103454 4.033308503247484 12.47566986144667 3.3715894355783376 2.0083098623587654 3.5320914288062633
user_002 Jogging 1.4460349041e12 -2.29862 5.67201 -5.51872 -3.556223636363637 -0.1143610909090908 -2.2336276363636363 5.2836539044 32.171697440100004 30.4562704384 8.24085079241822 5.5614694400953235 1.257603636363637 5.786371090909091 3.285092363636364 3.1761520661157023 4.962956611570248 1.373829479338843 1.5815669061950428 33.48209040170846 10.791831837621952 11.354773319808565 25.18833329477783 2.847330828690515 3.3696844540414412 5.018797993023611 1.6874035761164294
user_002 Jogging 1.446034904166e12 -1.14901 -2.72014 1.57053 -3.9254900000000004 1.7180463636363634 -1.6866922727272722 1.3202239801000002 7.399161619599999 2.4665644809 3.34454033920956 6.142751883178885 2.7764800000000003 4.438186363636364 3.2572222727272724 2.130101818181818 4.048336429752066 2.1747557190082643 7.708841190400001 19.697498198367768 10.609496933950618 5.225022162017731 19.2436754831257 5.679544464708638 2.2858307378320317 4.386761388897931 2.3831794864652216
user_002 Jogging 1.446034904303e12 -19.58108 -12.87503 -9.84892 -13.954961818181816 -12.484857272727272 -6.87387 383.4186939664 165.7663975009 97.00122516639999 25.420195054989254 20.16898227588495 5.626118181818184 0.3901727272727289 2.9750499999999995 6.916658239669422 4.181031487603305 3.943508214876033 31.653205795785144 0.15223475710743928 8.850922502499998 49.76640175867421 23.384981400124193 16.336958474720095 7.054530583864118 4.835802043107657 4.041900354377888
user_002 Jogging 1.44603490436e12 -15.02096 -6.20729 -7.70298 -18.717131818181816 -9.833787272727273 -8.61221909090909 225.6292393216 38.530449144100004 59.335900880400004 17.98598313537795 23.016621933143078 3.6961718181818153 3.6264972727272724 0.9092390909090895 4.279207363636366 3.1048967768595035 2.2276457851239666 13.661686109521467 13.151482469098346 0.8267157244371875 24.770207500773985 11.33453922324981 8.910379694181366 4.976967701399516 3.366680742697443 2.9850259118107108
user_002 Jogging 1.446034904367e12 -12.68342 -5.51753 -6.70665 -18.309542727272728 -9.070864545454546 -8.340492727272725 160.8691428964 30.4431373009 44.9791542225 15.37177395162315 22.220551075809762 5.626122727272728 3.553334545454546 1.6338427272727252 4.0572033057851264 3.084944214876033 1.8875136363636358 31.653256942334718 12.626186391920665 2.6694420574619766 21.730019531200156 11.188363815690682 6.526346154230428 4.661546903250053 3.3449011668045863 2.554671437627631
user_002 Jogging 1.446034904376e12 -10.95901 -5.13432 -5.82529 -17.577972727272726 -8.269620909090909 -7.870198181818181 120.09990018009998 26.361241862399996 33.9340035841 13.431125999952497 21.076610019864965 6.618962727272727 3.135300909090909 2.0449081818181813 3.907088595041323 3.1112299999999995 1.5556150413223135 43.81066758502562 9.830111790546281 4.18164947206694 19.49493349054441 11.345591140185949 3.957218397868069 4.4153067266662696 3.3683217097222093 1.989275847605874
user_002 Jogging 1.446034904401e12 -7.7401 -3.48655 -2.8363 -14.588988181818182 -5.907696363636364 -6.295580909090909 59.90914801 12.1560309025 8.04459769 8.950406504874513 16.99071880628637 6.848888181818182 2.4211463636363644 3.4592809090909094 4.26622305785124 3.505834132231405 1.504627107438016 46.907269327048766 5.86194971414959 11.966624408000829 23.70208991383614 12.767608535055674 3.195596680140795 4.868479219821745 3.5731790516367457 1.7876231929970015
user_002 Jogging 1.446034904481e12 2.56806 1.26517 -1.87829 -2.8107182727272733 -1.194297818181818 0.2989964545454545 6.5949321636 1.6006551288999997 3.5279733241 3.4239685478403565 4.608302892383878 5.378778272727273 2.459467818181818 2.1772864545454547 5.678689809917356 2.3445062148760334 3.615093132231405 28.93125570716299 6.048981948672032 4.740576305147116 32.508980915233295 5.547095110902433 15.245666932265921 5.701664749459871 2.355227188808424 3.9045700060654465
user_002 Jogging 1.446034904538e12 2.72134 -2.6435 -3.41111 3.4424599090909087 -0.6090423636363635 -1.4950904545454546 7.405691395600001 6.98809225 11.635671432099999 5.101907004023103 4.55478708374157 0.7211199090909086 2.034457636363636 1.9160195454545452 4.419503983471075 1.9660537438016528 2.015458099173554 0.5200139232872804 4.139017874158314 3.6711308985638422 22.016640849837806 4.48710159313118 4.649995244198693 4.692189345053949 2.1182779782481758 2.1563847625594774
user_002 Jogging 1.446034904765e12 -13.10495 -10.1926 -1.95493 -14.696981818181818 -12.634653636363636 -0.47089309090909093 171.73971450250002 103.88909476 3.8217513049000003 16.7167748255278 19.43928532597381 1.5920318181818178 2.442053636363635 1.4840369090909091 2.847736140495868 3.617310611570248 0.5342670909090909 2.5345653101033045 5.963625962876853 2.2023655475440993 10.064474543588254 16.68699578470033 0.410335260510263 3.172455601515686 4.084971944175423 0.6405741647227611
user_002 Jogging 1.446034904773e12 -12.03198 -9.19628 -2.8363 -14.679563636363637 -12.31067272727273 -0.6590108181818182 144.7685427204 84.57156583839999 8.04459769 15.407293930109855 19.232055710552334 2.6475836363636365 3.1143927272727296 2.177289181818182 2.7045890909090913 3.2676766776859507 0.6831144380165289 7.009699111540496 9.699442059689272 4.7405881812624875 9.081085115569495 13.164518257948806 0.8147918375588407 3.013483883409615 3.628294125060537 0.9026582063875788
user_002 Jogging 1.446034904789e12 -10.38421 -7.20362 -2.22318 -14.254558181818181 -11.439757272727274 -1.052665090909091 107.83181732409999 51.8921411044 4.9425293124000005 12.83224406488982 18.390656255115662 3.8703481818181817 4.236137272727274 1.170514909090909 2.6713357024793383 3.084626363636364 0.8677489999999999 14.979595048503306 17.944858993389268 1.370105152404099 8.862194919781967 11.457581575641553 1.217527360808707 2.976943889256559 3.384904958140118 1.1034162228319406
user_002 Jogging 1.446034904813e12 -5.82409 -7.24194 -0.690364 -11.965790909090911 -9.454068181818185 -1.383612909090909 33.9200243281 52.4456949636 0.476602452496 9.318922778100267 15.389952193371483 6.141700909090911 2.2121281818181853 0.6932489090909091 3.0798742148760336 2.510138595041323 0.8997350330578513 37.720490056728124 4.89351109279423 0.4805940499557355 12.78673982575342 7.319570001085881 1.251892622913894 3.575855118115584 2.7054703844407317 1.1188800753047192
user_002 Jogging 1.44603490487e12 -3.25663 4.5224 -4.67568 -6.130652727272727 -2.486738545454545 -2.303301818181818 10.6056389569 20.45210176 21.861983462399998 7.274594434007988 8.44300942622068 2.874022727272727 7.009138545454546 2.3723781818181817 4.0055809090909085 5.034529355371902 0.8322801074380163 8.260006636880163 49.128023149376666 5.628178237566941 18.04848911271097 29.640567436933203 1.0455075809433545 4.248351340545056 5.4443151485685695 1.0225006508278391
user_002 Jogging 1.446034904894e12 -0.804128 1.34181 -2.0699 -4.075289818181819 0.38380145454545445 -2.7352758181818184 0.646621840384 1.8004540760999999 4.28448601 2.5945253759568434 6.449416857876946 3.271161818181819 0.9580085454545455 0.6653758181818183 3.617944710743801 5.087417801652894 0.9158868429752065 10.700499640730584 0.917780373163934 0.4427249794211242 14.79149537720143 30.924407254086645 1.2617954625082854 3.84597131778195 5.560971790441545 1.1232966938918165
user_002 Jogging 1.446034904942e12 -0.957409 -2.4519 -1.22685 -1.6854947272727272 0.575403727272727 -1.5543139090909088 0.9166319932809999 6.011813610000001 1.5051609225 2.9040672385089503 3.9559630267711743 0.7280857272727272 3.0273037272727272 0.32746390909090883 2.25044847107438 3.949843132231405 1.8406406776859507 0.5301088262582562 9.164567857159346 0.107232611757099 5.822947048104639 20.150232924354416 4.563080723516522 2.4130783344319013 4.488901082041619 2.136136869097231
user_002 Jogging 1.446034905113e12 -16.70706 -5.51753 -6.13185 -18.264255454545456 -11.896116363636365 -8.065281818181818 279.12585384359994 30.4431373009 37.5995844225 18.632460266078656 23.416310510578196 1.5571954545454574 6.378586363636365 1.933431818181818 3.513750330578513 3.527368347107439 2.832853694214876 2.4248576836570335 40.68636399836778 3.7381585955578505 25.832541611438845 14.991027844016308 10.362856133310423 5.0825723419779125 3.8718248725912576 3.219139036032837
user_002 Jogging 1.446034905169e12 -7.89339 0.728685 1.37893 -13.693688181818182 -3.695569454545455 -4.693093454545454 62.3056056921 0.530981829225 1.9014479449 8.045994995413867 15.34229944936368 5.800298181818182 4.424254454545455 6.0720234545454534 3.043455371900826 5.645120239669422 2.632384115702479 33.643458998003304 19.574027478565302 36.869468832550105 13.436308781997292 32.79240188340361 10.397747111488627 3.66555709026572 5.726465042537465 3.224553784865222
user_002 Jogging 1.446034905493e12 -15.44249 -13.64143 -0.11556 -15.313590909090909 -13.67975090909091 1.054952090909091 238.4704974001 186.08861244489998 1.3354113599999998e-2 20.60515624688636 21.085682903240833 0.12889909090909057 3.8320909090909794e-2 1.170512090909091 2.6067309917355375 1.5084261983471072 3.4773302066115708 1.6614975637189996e-2 1.468492073553773e-3 1.3700985549643718 14.628895633531561 3.0635775120513133 19.6558582853718 3.8247739323431342 1.7503078335113835 4.433492786209514
user_002 Jogging 1.446034905501e12 -14.906 -12.10862 -0.1922 -15.111538181818183 -13.700652727272727 0.25022572727272735 222.188836 146.6186783044 3.694084e-2 19.205323614675176 20.7796444806875 0.2055381818181825 1.592032727272727 0.44242572727272733 1.8586934710743805 1.4092996694214877 2.8122669752066116 4.224594418512425e-2 2.5345682047074374 0.19574052415280171 8.166233634188808 2.6398653995649872 14.201975998263556 2.857662267341753 1.624766259978643 3.768550914909278
user_002 Jogging 1.446034905631e12 -1.34061 4.40743 -4.13919 -5.099487272727273 -2.1732090909090913 -2.3729745454545452 1.7972351721000002 19.425439204899998 17.1328938561 6.193187243503946 7.331724758582661 3.758877272727273 6.5806390909090915 1.766215454545455 4.159495123966942 4.7365159504132235 0.7170017685950415 14.12915835142562 43.30481084480083 3.119517031875208 17.9341842130411 25.112124580614953 0.9352357872741565 4.234877119001341 5.011199914253567 0.9670758953019957
user_002 Jogging 1.446034905663e12 -2.18366 -0.420925 -3.29615 -2.772398818181818 0.8157759090909089 -3.243890909090909 4.768370995600001 0.177177855625 10.864604822499999 3.976198394663551 5.5856101440878625 0.5887388181818181 1.236700909090909 5.2259090909090755e-2 3.2746450495867765 4.383083636363636 1.011529834710744 0.34661339603412383 1.5294291385462806 2.731012582644612e-3 12.606584914941841 23.25747815560631 1.7777824431994913 3.5505752935181984 4.822600766765409 1.333335082865328
user_002 Jogging 1.446034905719e12 -0.229323 -3.33327 4.02303 -1.9885736363636364 -1.3545477272727275 -0.1956850909090907 5.2589038329e-2 11.1106888929 16.1847703809 5.229536146937796 5.172272803925215 1.7592506363636364 1.9787222727272726 4.218715090909091 1.1581613553719008 3.279396074380165 3.183435008264463 3.0949628015458597 3.915341832586983 17.797557018264104 2.2964233602852517 12.828385137281272 12.516466305779879 1.515395446834011 3.581673510704357 3.537861826835508
user_002 Jogging 1.446034905809e12 -19.58108 -11.72542 -10.23212 -11.652259727272728 -11.49201090909091 -4.919532454545455 383.4186939664 137.4854741764 104.6962796944 25.012006073827827 18.2206364433844 7.928820272727272 0.23340909090909 5.312587545454545 7.430340818181818 4.184197314049587 4.264320454545454 62.86619091721097 5.447980371900785e-2 28.22358642811875 69.60503321583221 22.851830057978496 21.710520234285465 8.34296309567723 4.780358779210876 4.6594549288822895
user_002 Jogging 1.44603490589e12 -10.72909 -2.33694 -6.05521 -16.79414909090909 -7.332516363636364 -7.96774 115.11337222809999 5.461288563599999 36.6655681441 12.539546600088856 20.12150734565 6.065059090909092 4.9955763636363635 1.9125300000000003 3.6692487272727266 3.119780082644628 2.1247186446281 36.784941776219014 24.955783204922312 3.6577710009000013 18.701081109706283 13.284676463152287 7.08943210848389 4.324474662858632 3.644815010827338 2.6625987509356137
user_002 Jogging 1.44603490593e12 -4.82776 -0.574206 -5.99e-4 -11.269057272727274 -3.068510363636363 -4.494526545454545 23.307266617599996 0.329712530436 3.5880100000000004e-7 4.861787686318377 12.660603854836262 6.441297272727274 2.4943043636363633 4.493927545454545 4.729232892561983 4.135426595041323 2.612748289256199 41.49031055564382 6.221554258455403 20.19538478379511 26.98205981281337 18.009014885965737 9.086475011597456 5.19442584053458 4.243702968630785 3.0143780472259043
user_002 Jogging 1.446034906132e12 -15.74905 -17.81835 0.344284 -8.572700272727273 -9.20672818181818 -1.6274719090909096 248.0325759025 317.49359672249994 0.11853147265599999 23.78328623419514 13.337573546264622 7.1763497272727275 8.611621818181819 1.9717559090909096 7.523449586776858 4.22220267768595 1.909365611570248 51.49999540812735 74.16003033938513 3.8878213650349194 61.7491867891929 25.090541422510398 5.45840222276125 7.858065079215932 5.009045959313051 2.336322371326622
user_002 Jogging 1.446034906521e12 -16.36218 -11.4955 -7.5497 -4.873049363636364 -7.747071818181819 -0.7495861818181818 267.7209343524 132.14652025 56.997970089999995 21.374410510991876 10.57141105888111 11.489130636363635 3.7484281818181806 6.800113818181818 4.584187264462809 4.209851421487603 3.757607553719008 132.00012277942946 14.050713834248752 46.2415479402273 38.234762361468455 24.94539292302512 16.971525438143534 6.183426425653374 4.994536307108511 4.119651130635158
user_002 Jogging 1.446034906529e12 -17.12858 -10.46085 -8.27779 -6.38147609090909 -8.294007272727272 -1.606568 293.3882528164 109.42938272250001 68.52180728409999 21.710353355553657 12.124911226676351 10.74710390909091 2.166842727272728 6.671221999999999 5.3670615123966945 4.060687322314049 4.055619611570248 115.50024243279712 4.695207404734715 44.50520297328399 48.32021117320367 24.054213422791477 19.97081157847642 6.951274068341981 4.904509498695203 4.468871398740002
user_002 Jogging 1.446034906715e12 1.99325 -0.344284 -0.1922 -6.9562799090909095 -0.9434740909090908 -2.592445181818182 3.9730455625 0.11853147265599999 3.694084e-2 2.031875457589859 7.956944177253901 8.94952990909091 0.5991900909090908 2.400245181818182 6.556257595041322 2.1237692975206617 3.3148641404958683 80.09408559371273 0.3590287650436445 5.761176932841397 47.557804477929864 6.570856032718509 11.231214085224345 6.896216678580355 2.563368103242004 3.351300357357476
user_002 Jogging 1.446034906764e12 5.55704 3.8919e-2 -1.57173 1.648371909090909 0.29671036363636366 -1.0456967272727273 30.880693561599998 1.514688561e-3 2.4703351929000004 5.775166096577742 3.927382842329911 3.9086680909090905 0.2577913636363637 0.5260332727272727 7.148796636363636 0.9941112479338842 1.907780231404959 15.277686244890914 6.645638716549589e-2 0.2767110040161653 53.543776224592506 1.218222511930528 5.9435548466332 7.317361288373871 1.103731177384479 2.4379406979320066
user_002 Jogging 1.446034906788e12 3.41111 -2.60518 -3.8919e-2 3.8744337272727276 -0.14223127272727273 -1.0038927272727272 11.635671432099999 6.7869628323999995 1.514688561e-3 4.2923360717750185 4.281714191828106 0.46332372727272775 2.4629487272727273 0.9649737272727271 5.373076958677687 1.2151654049586775 1.0077278181818183 0.214668876253893 6.066116433174347 0.9311742943266196 36.83587198966369 1.9644262833778166 2.035507535520235 6.069256296257696 1.4015799240064108 1.426712141786224
user_002 Jogging 1.446034906869e12 -9.15796 -6.59049 -4.59904 -4.7615704545454545 -3.653766363636364 -1.1258220909090908 83.86823136159998 43.4345584401 21.151168921599997 12.184168364041101 7.534283163932319 4.396389545454545 2.9367236363636358 3.4732179090909088 5.570380008264463 1.7925042231404957 1.193629347107438 19.328241035382018 8.624345716376856 12.063242644029824 39.045948739142915 4.770132105713073 2.186160728735234 6.2486757588422615 2.1840632101001733 1.4785671201319317
user_002 Jogging 1.446034907055e12 -8.96635 -6.28393 -2.37646 -14.055988181818185 -11.060037272727273 -0.8680313636363636 80.3954323225 39.4877762449 5.647562131599999 11.204051530540191 17.980667829343247 5.089638181818184 4.776107272727273 1.5084286363636363 3.1850199173553735 1.969853553719008 0.9963280909090908 25.904416821821513 22.811200680598354 2.2753569510018594 12.3243425505523 5.979313249989634 1.477317282096447 3.5106042999108147 2.445263431614196 1.2154494156880602
user_002 Jogging 1.446034907176e12 -3.17999 2.10822 -2.72134 -3.253144545454545 1.756367909090909 -2.9408118181818184 10.1123364001 4.444591568400001 7.405691395600001 4.686429276549472 5.4434715507149125 7.31545454545448e-2 0.3518520909090912 0.21947181818181827 2.009758181818181 3.9077233719008264 0.8763001735537188 5.3515875206610625e-3 0.12379989387709937 4.81678789760331e-2 8.371246828439217 17.596841194972075 1.1728786380655 2.893310703750846 4.194858900484268 1.0829952160861562
user_002 Jogging 1.446034907217e12 -2.60518 -3.44823 -0.1922 -3.1695363636363636 1.3557463636363638 -2.0873139999999997 6.7869628323999995 11.8902901329 3.694084e-2 4.325990499908662 5.171482505680273 0.5643563636363638 4.803976363636364 1.8951139999999997 0.4522432231404956 3.8599021983471076 1.5062108264462812 0.31849810517685967 23.078188902376866 3.591457072995999 0.2748354196277234 17.748269714747806 2.709150374558628 0.5242474793718358 4.2128695345035085 1.645949687736119
user_002 Jogging 1.446034907282e12 -12.98999 -15.71073 -5.0972 -5.245800909090909 -6.998084545454546 -1.1084039090909092 168.73984020010002 246.8270371329 25.98144784 21.01305130562908 9.044514809492759 7.744189090909091 8.712645454545454 3.9887960909090907 2.1218685123966945 5.465871355371901 2.3274055785123964 59.972464675755376 75.91019081661156 15.910494254851644 12.08835882428768 34.59527934232356 6.941450569358176 3.4768317221700102 5.881775186312679 2.634663274378374
user_002 Jogging 1.44603490737e12 -19.15956 -7.85507 -7.05154 -18.156263636363633 -11.809024545454546 -8.901361818181819 367.08873939359995 61.70212470490001 49.7242163716 21.874987553598743 23.72199698592232 1.003296363636366 3.953954545454546 1.8498218181818187 5.370544462809917 3.4079715702479345 3.8684508181818176 1.0066035932859554 15.633756547520665 3.4218407590214897 36.820366186531174 15.250190459474835 18.943982616096033 6.067978756268942 3.9051492237140994 4.352468565779199
user_002 Jogging 1.446034907403e12 -16.32385 -2.98839 -6.70665 -18.60913818181818 -8.074537272727271 -9.162636363636363 266.4680788225 8.9304747921 44.9791542225 17.899097961548232 22.465247190479637 2.2852881818181814 5.086147272727271 2.455986363636363 2.8151174380165287 3.4934809917355367 3.2850951074380172 5.222542073957849 25.868894079871062 6.0318690183677655 13.08808219941119 15.12350955082885 15.124677542114034 3.6177454580734656 3.888895672402237 3.8890458395490834
user_002 Jogging 1.44603490763e12 -7.77842 -0.804128 2.33694 -1.309259 -1.4346706363636363 -0.27232436363636364 60.50381769639999 0.646621840384 5.461288563599999 8.161600829517699 4.856999590605138 6.469161 0.6305426363636364 2.6092643636363633 3.561889454545455 0.643527520661157 1.4802419504132232 41.850044043920995 0.39758401627240497 6.808260519342676 20.831291931262594 0.5178461229852592 3.4899073511287853 4.564131016005412 0.719615260389369 1.8681293721605003
user_002 Jogging 1.446034907654e12 -8.31491 -7.62514 -6.47673 -4.3923026363636355 -2.256814909090909 -1.2094304545454546 69.1377283081 58.1427600196 41.9480314929 13.008786254704933 6.817305834917863 3.922607363636364 5.3683250909090905 5.267299545454545 4.743168247933884 1.1372572975206612 2.2691339586776857 15.386848529254225 28.818914281684094 27.744444501545658 27.438662371744726 3.279949445254316 7.294591790096374 5.23819266271724 1.8110630704794122 2.7008501976408046
user_002 Jogging 1.446034907678e12 -14.82936 -13.948 3.63983 -8.067568181818181 -5.447853090909091 -0.7112665454545454 219.90991800959998 194.546704 13.248362428899998 20.681029578783065 10.8121546065273 6.761791818181818 8.500146909090908 4.351096545454546 5.643219752066115 3.4941161239669416 2.729611066115702 45.721828592430576 72.25249747612773 18.93204114786648 33.4239033673911 27.913006124494846 9.746806300428416 5.781340966193838 5.283276078769199 3.1219875560976242
user_002 Jogging 1.446034907904e12 -4.3296 2.75966 -1.30349 -7.5589545454545455 -2.8560068181818186 -2.797982727272727 18.74543616 7.615723315599999 1.6990861801000001 5.297192242660256 8.883504805448565 3.2293545454545454 5.615666818181818 1.494492727272727 4.654491239669421 4.516412933884298 1.1739957190082644 10.428730780247934 31.53571381282831 2.233508511871074 23.339964729773104 20.7930003177753 2.0841700125165734 4.831145281377192 4.559934244896005 1.4436654780511216
user_002 Jogging 1.446034907913e12 -3.63983 4.56072 -1.34181 -6.733325454545454 -1.8318086363636361 -2.6168318181818178 13.248362428899998 20.8001669184 1.8004540760999999 5.987402059608157 8.085788948485714 3.0934954545454545 6.392528636363636 1.2750218181818178 4.686161570247934 4.656393636363637 1.0932376942148758 9.569714127293388 40.86442236672913 1.6256806368396686 23.52487566892179 22.36712104831754 1.8064930810530717 4.850244908138329 4.729389077705231 1.3440584366213664
user_002 Jogging 1.446034907936e12 -3.06503 3.18118 -3.33447 -4.468944545454546 0.7042995454545454 -2.491420909090909 9.3944089009 10.1199061924 11.1186901809 5.534709140885363 6.1632089767866995 1.4039145454545459 2.4768804545454546 0.8430490909090911 4.319109421487604 4.469225578512397 0.7322038429752066 1.970976050938844 6.134936786109297 0.710731769682645 21.374971039417286 21.089082884775454 0.7007315357295453 4.6233073702077485 4.592285148460999 0.8370970885922047
user_002 Jogging 1.446034908074e12 -9.69444 -11.8787 -0.805325 -4.068322727272728 0.3489659090909093 -2.3416238181818185 93.9821669136 141.10351369 0.6485483556249999 15.353638948445576 6.256494405692689 5.626117272727273 12.22766590909091 1.5362988181818187 3.350651404958678 4.778638016528926 0.9405909669421487 31.653195566480164 149.51581358434402 2.3602140587468527 14.281345570168895 30.914827648535017 1.0798813779074146 3.779066759157464 5.560110398952077 1.0391734108932034
user_002 Jogging 1.446034908139e12 -16.20889 -13.83303 -8.43107 -5.102970909090908 -0.7588395454545455 -2.811918363636364 262.7281150321 191.35271898090002 71.08294134490001 22.91645206741 7.7895724282934165 11.105919090909092 13.074190454545455 5.619151636363636 3.8196790082644627 5.613133347107438 1.4023345041322315 123.34143885381903 170.9344560417275 31.57486511244813 22.279454978312547 45.07532239502894 3.9238172475664856 4.720111754854174 6.713815785008473 1.9808627533391823
user_002 Jogging 1.446034908463e12 -9.38788 -8.92803 -0.920286 -5.604617272727274 -3.486549818181818 -2.428715181818182 88.13229089439999 79.7097196809 0.8469263217960001 12.988030524182486 9.187988234579967 3.7832627272727253 5.441480181818182 1.5084291818181819 4.455290578512398 4.438821066115702 2.185842553719008 14.313076863571059 29.609706569120036 2.2753585965606695 32.435867004961985 37.61418130025047 6.970272935876789 5.695249512090053 6.1330401352225365 2.6401274469003932
user_002 Jogging 1.446034908916e12 -16.43882 -15.02096 -10.73029 -7.273292727272727 -6.155037090909091 -1.672757909090909 270.2348029924 225.6292393216 115.1391234841 24.718478225774742 11.284802730750444 9.165527272727273 8.865922909090909 9.057532090909092 5.137139504132232 4.605721454545455 2.7612792479338846 84.00689018710744 78.604589029943 82.03888757784803 38.23730245817776 30.93058873133441 12.517200853787648 6.183631817805598 5.561527553769235 3.537965637734155
user_002 Jogging 1.446034908981e12 -14.5228 -4.86608 -7.05154 -8.25917 -6.4372134545454545 -2.449615181818182 210.91171984000002 23.678734566400003 49.7242163716 16.861633099376824 12.42281859930853 6.263630000000001 1.5711334545454543 4.601924818181818 5.498807190082645 4.714031438016529 2.795482975206612 39.23306077690001 2.468460331991933 21.177712032197757 41.32916892800894 31.141886030605203 12.8191379720562 6.4287766276336695 5.5804915581519525 3.58038237791108
user_002 Jogging 1.446034911117e12 -4.138 1.57173 -2.87462 -8.47515909090909 -6.597462727272728 -2.5053534545454546 17.123044 2.4703351929000004 8.2634401444 5.277955980993021 12.378208799153429 4.33715909090909 8.169192727272728 0.3692665454545456 5.41583082644628 5.39176394214876 2.1766558512396696 18.81094897985536 66.73570981532563 0.136357781591934 44.27695044952525 35.340990234223725 8.265993487591441 6.654092759311765 5.9448288650072785 2.8750640840842907
user_002 Jogging 1.446034911505e12 -0.880768 -7.6042e-2 0.459245 -9.063898 -6.924927454545455 -2.4043275454545454 0.775752269824 5.782385764e-3 0.210905970025 0.9962131426622518 12.229235132780667 8.18313 6.848885454545455 2.8635725454545455 4.822659256198348 5.042447603305785 2.4689677851239673 66.96361659690001 46.9072319694843 8.200047723081026 32.30563775185838 33.39696622379565 9.388849709188909 5.683804865744282 5.779010834372579 3.0641229918508346
user_002 Jogging 1.446034912671e12 -6.13065 -0.420925 -3.10454 -8.461222636363637 -6.231678 -2.132602181818182 37.5848694225 0.177177855625 9.638168611600001 6.884781470005057 12.102373588962756 2.3305726363636365 5.810753 0.9719378181818179 5.907028347107438 4.40873579338843 2.5066566363636364 5.431568813366951 33.764850427009 0.9446631224120325 50.828857630514584 25.11324930487152 9.586059643286172 7.129435996663031 5.011312134049477 3.096136244302917
user_002 Jogging 1.446034913448e12 -7.12698 -0.727487 -2.2615 -8.994222636363636 -6.663652454545454 -2.1604711818181817 50.79384392039999 0.529237335169 5.114382249999999 7.5124871717407276 12.297534620940462 1.8672426363636365 5.936165454545454 0.10102881818181819 5.128271347107439 4.81854147107438 2.129470016528926 3.4865950630542235 35.238060303738834 1.0206822103214878e-2 38.6690300335663 30.39342674095808 6.766964182928945 6.218442733801309 5.513023375694872 2.601338921195957
user_002 Jogging 1.446034915132e12 -3.79311 -0.650847 0.267643 -8.910616363636363 -4.698865454545454 -0.1364618181818182 14.387683472099999 0.42360181740899994 7.163277544900001e-2 3.8578385224057783 10.584969232379587 5.1175063636363625 4.0480184545454545 0.4041048181818182 4.847044462809918 4.361232578512396 1.7323318264462806 26.188871381858664 16.38645340834057 0.16330070407776034 29.31876509625081 22.243799336105926 4.342268189926172 5.4146805165448875 4.716333251171499 2.083810977494401
user_002 Jogging 1.446034915197e12 -9.57948 -6.93538 7.6042e-2 -8.52393 -4.493329090909091 0.31293109090909094 91.7664370704 48.0994957444 5.782385764e-3 11.826737301579165 10.086547002310532 1.0555500000000002 2.4420509090909093 0.23688909090909094 4.456240859504132 4.307077289256198 1.427036123966942 1.1141858025000004 5.963612642591737 5.611644139173555e-2 26.813737589387326 21.947038640486916 3.1723656216127227 5.178198295680393 4.684766658061735 1.781113590317227
user_002 Jumping 1.446035035287e12 -15.55745 -19.38948 1.26397 -6.910992181818182 -8.753850818181819 0.2850607272727273 242.0342505025 375.95193467039996 1.5976201609 24.89144040295378 11.624306276171978 8.646457818181817 10.63562918181818 0.9789092727272728 4.716565537190082 6.76115967768595 0.7705225371900827 74.76123280159747 113.11660809314245 0.9582633642314381 27.958317956097122 53.20256051849058 0.6330625595010736 5.287562572310338 7.2940085356743705 0.7956522855500847
user_002 Jumping 1.446035035351e12 -14.75272 -19.46612 0.995729 -7.381286727272727 -9.38787809090909 0.29551172727272723 217.6427473984 378.9298278544 0.991476241441 24.445123266088086 12.413256938175369 7.371433272727273 10.07824190909091 0.7002172727272727 5.027878347107438 7.162414743801653 0.787307570247934 54.338028494270716 101.57095997815638 0.4903042290256199 31.481888844794117 59.51938985669653 0.6534697889596003 5.610872378230868 7.714881065622238 0.8083747824861933
user_002 Jumping 1.44603503561e12 -0.420925 -1.30229 -0.307161 -4.848662272727272 -6.008723000000001 -8.420718181818178e-2 0.177177855625 1.6959592440999998 9.434787992100001e-2 1.402670659722374 8.259123344540706 4.427737272727272 4.7064330000000005 0.22295381818181825 4.2412035206611565 6.341853776859505 0.7100340247933885 19.604857356298343 22.150511583489006 4.970840504185127e-2 22.47600091925477 45.354138884615956 0.573384619427679 4.740886090094843 6.734548157420508 0.7572216448489035
user_002 Jumping 1.446035036388e12 -5.63249 -10.38421 0.229323 -5.413016636363636 -6.750744090909091 -0.36638345454545457 31.724943600099998 107.83181732409999 5.2589038329e-2 11.815640057251615 9.290682276237781 0.2194733636363635 3.6334659090909085 0.5957064545454546 4.421087884297521 5.95073317355372 0.7208016280991736 4.816855734585944e-2 13.202074512525822 0.3548661799871157 26.6963255865405 41.226568967934206 0.7234207346930931 5.166848709468906 6.420791926852497 0.8505414361999615
user_002 Jumping 1.446035036453e12 -12.6451 -17.97163 1.26397 -6.409344818181818 -8.192981363636365 -7.375618181818186e-2 159.89855400999997 322.97948485690006 1.5976201609 22.010807777721382 10.988756568301302 6.235755181818181 9.778648636363636 1.3377261818181818 4.689329272727273 6.469166107438017 0.6843818347107438 38.884642687572295 95.6219691534564 1.7895113375218512 29.250212975164427 48.40921619558689 0.6113908975338558 5.40834660272106 6.9576731883286165 0.7819148914900239
user_002 Jumping 1.44603503736e12 0.268841 -0.995729 -0.958607 -4.831242636363636 -5.886794363636364 -0.4221228181818182 7.2275483281e-2 0.991476241441 0.918927380449 1.40807638470752 8.342801136380048 5.100083636363636 4.891065363636364 0.5364841818181818 4.486643495867768 6.314617280991735 0.684381867768595 26.01085309790413 23.922520391363317 0.28781527734112394 24.721975480839447 45.716738325488144 0.7141433950516395 4.972119817627029 6.761415408439873 0.845070053339745
user_002 Jumping 1.446035037424e12 -1.49389 3.8919e-2 -0.460442 -4.886981 -6.008722636363634 -0.4116718181818182 2.2317073320999996 1.514688561e-3 0.21200683536400003 1.5637227554860866 8.32719446672629 3.3930909999999996 6.047641636363634 4.8770181818181824e-2 4.467958479338843 6.213274247933884 0.6476450247933885 11.513066534280998 36.573969361879016 2.378530634578513e-3 24.5913351297316 44.37799111909305 0.6957145180793509 4.958965126892061 6.661680802852464 0.8340950294057332
user_002 Jumping 1.446035037683e12 -16.89866 -19.58108 -0.690364 -7.335999 -9.234596181818183 -0.2897431818181818 285.5647097956 383.4186939664 0.476602452496 25.873925218537984 12.289344042912308 9.562660999999999 10.346483818181817 0.40062081818181816 5.574496611570248 6.9480109586776875 0.49309669421487606 91.44448540092097 107.04972739989819 0.1604970399606694 38.60496422999283 57.953553301972086 0.3831870005899715 6.213289324503796 7.61272312001245 0.6190210017357825
user_002 Jumping 1.446035037813e12 -1.68549 -1.83878 0.382604 -5.865892636363636 -7.395221636363636 -0.36638363636363636 2.8408765400999996 3.3811118884000004 0.146385820816 2.5235637993353763 9.925484171249254 4.180402636363636 5.556441636363636 0.7489876363636363 4.904050214876033 6.237026396694215 0.4500260495867768 17.47576620211604 30.8740436583154 0.5609824794255867 29.490202021043206 46.183238745060336 0.2788734853397626 5.430488193619723 6.795825096709033 0.5280847331061206
user_002 Jumping 1.446035040208e12 -0.459245 0.920286 -1.34181 -5.315474000000001 -6.677586363636363 -0.6137239999999999 0.210905970025 0.8469263217960001 1.8004540760999999 1.6906467306687698 9.261843463669647 4.856229000000001 7.5978723636363625 0.728086 4.325128140495868 5.7214437024793385 0.6352940247933886 23.582960100441007 57.72766445410921 0.530109223396 23.31046909148014 42.84138752310991 0.4917808251254432 4.828091661462129 6.545333262952308 0.7012708643066837
user_002 Jumping 1.446035040531e12 -9.65612 -12.60678 -1.15021 -6.005239272727272 -7.621659636363637 -0.746102909090909 93.24065345439999 158.9309019684 1.3229830441 15.92151181473983 10.210010521380092 3.6508807272727273 4.985120363636364 0.4041070909090909 4.329245619834711 5.909877884297521 0.5887393388429752 13.328930084771438 24.851425039941955 0.16330254092300828 22.52924776787061 44.68324583485345 0.4008151098503697 4.746498474440987 6.684552777475353 0.633099604999379
user_002 Jumping 1.446035041049e12 -2.72014 -3.37159 -1.76333 -5.3955969999999995 -6.377990545454546 -0.6938477272727273 7.399161619599999 11.3676191281 3.1093326889000004 4.677190763332194 8.884110392773467 2.6754569999999998 3.006400545454546 1.0694822727272728 4.5788023388429755 5.791433371900829 0.5086150413223138 7.158070158848998 9.038444239709392 1.1437923316778926 26.28320640632546 37.88538753004604 0.3918992896498903 5.126714972214221 6.155110683817639 0.6260186016804056
user_002 Jumping 1.446035042602e12 1.64837 1.53341 -1.26517 -4.392303181818181 -6.851770272727273 -0.7391359090909091 2.7171236568999997 2.3513462280999997 1.6006551288999997 2.5824649104876523 8.912902370235305 6.040673181818181 8.385180272727272 0.5260340909090908 3.7911784380165288 6.163553950413223 0.4873965289256199 36.48973248953739 70.31124820613461 0.27671186479855364 17.489989493492825 43.924118922545375 0.29041824755649287 4.182103477138368 6.627527361131403 0.5389046739048502
user_002 Jumping 1.446035042668e12 0.422122 -1.18733 -0.728685 -4.364433909090908 -6.844803 -0.7286849090909091 0.178186982884 1.4097525289 0.530981829225 1.4556515177091665 8.906684790307402 4.786555909090908 5.6574729999999995 9.0909090921798e-8 3.777243776859504 6.1201664876033055 0.4560435537190083 22.911117470853092 32.007000745728995 8.264462812227734e-15 17.35445550149097 43.41248493255424 0.2796051422585815 4.165867916952117 6.58881513874492 0.5287770250857932
user_002 Jumping 1.446035043121e12 -4.3296 -6.74378 0.114362 -5.043748636363636 -7.980478090909091 -0.9655744545454547 18.74543616 45.4785686884 1.3078667044000002e-2 8.014804022273033 10.159283198878056 0.7141486363636362 1.2366980909090906 1.0799364545454546 3.8741517190082644 6.2810481570247925 0.9665591404958679 0.5100082748200412 1.5294221680581892 1.1662627458562067 20.302119742441093 47.49064113773937 1.4988273611587017 4.50578736098821 6.891345379368195 1.2242660499902387
user_002 Jumping 1.44603504338e12 -1.95374 -0.612526 -1.34181 -4.347015636363637 -6.057495727272727 -0.937705 3.8170999876000002 0.375188100676 1.8004540760999999 2.4480077949990275 8.273893755622877 2.3932756363636374 5.444969727272727 0.40410499999999994 3.9118382975206614 6.211057958677685 1.0739194297520658 5.727768271611773 29.647695330916434 0.16330085102499994 19.778612203884183 46.26945035536362 1.6057372723978836 4.447315168040622 6.80216512261821 1.2671768907291057
user_002 Jumping 1.44603504448e12 -0.459245 -0.229323 -1.18853 -5.287603090909091 -6.9771812727272735 -0.9307369090909091 0.210905970025 5.2589038329e-2 1.4126035609000003 1.2946422553176613 9.476152949648709 4.828358090909091 6.747858272727274 0.25779309090909097 4.262104669421488 6.1702033719008265 0.6112244876033058 23.313041854047277 45.5335912688139 6.645727772046284e-2 23.640955114855853 45.134428060760406 0.4930197020222338 4.862196531903647 6.718216136800036 0.7021536171111232
user_002 Jumping 1.446035044739e12 -11.18893 -16.89866 -1.03525 -6.3954082727272725 -8.757333454545455 -0.8854496363636364 125.19215454489998 285.5647097956 1.0717425625 20.293560725092085 11.359921231515365 4.793521727272727 8.141326545454545 0.14980036363636362 4.538898115702478 6.712388214876032 0.5801884545454545 22.977850549835704 66.28119791972283 2.2440148945586772e-2 25.736066941496144 50.24123463081261 0.45139800147421877 5.07307273173726 7.088105150942148 0.6718615939866028
user_002 Jumping 1.446035046163e12 0.11556 1.41845 -1.45677 -4.918334727272727 -6.743776545454546 -0.8715144545454545 1.3354113599999998e-2 2.0120004025 2.1221788328999995 2.036549373081831 9.056364871324707 5.0338947272727275 8.162226545454546 0.5852555454545454 4.4670074462809914 6.255394834710743 0.7227016694214875 25.340096125264168 66.62194217932286 0.34252405348529746 22.30188578895255 43.665427425798704 0.8360514631476093 4.722487246033868 6.607982099385462 0.9143584981546402
user_002 Jumping 1.446035046551e12 -15.21256 -19.58108 -0.996927 -7.221037636363636 -9.311237181818182 -0.9168020909090909 231.4219817536 383.4186939664 0.993863443329 24.816013764570027 12.226709343990398 7.9915223636363635 10.269842818181818 8.012490909090908e-2 4.73936579338843 6.616745652892562 0.7619723223140497 63.86442968850013 105.46967151016067 6.420001056826444e-3 27.295248065600617 51.45718724716073 0.87134305900294 5.224485435485549 7.1733665211782345 0.9334575828621995
user_002 Jumping 1.44603504694e12 -0.650847 -0.535886 0.152682 -5.015878818181817 -6.398894181818182 -0.606755909090909 0.42360181740899994 0.287173804996 2.3311793124000002e-2 0.8567890145940247 8.614114338184608 4.3650318181818175 5.8630081818181825 0.759437909090909 4.247853950413224 5.7736992644628105 0.5811379752066116 19.053502773739663 34.37486494006695 0.5767459377643718 22.57831495566934 40.71143977129847 0.4586385032268108 4.751664440558629 6.380551682362464 0.67722854578555
user_002 Jumping 1.446035047134e12 -15.28921 -19.50444 -1.18853 -7.189685909090909 -9.227629636363638 -0.6276584545454545 233.75994242410002 380.42317971359995 1.4126035609000003 24.81120161738645 12.127786396150414 8.099524090909092 10.276810363636361 0.5608715454545455 5.05701467768595 6.479300024793388 0.5304669421487603 65.60229049921676 105.61283125014371 0.31457689050057036 30.71943408184397 50.9383244056931 0.4049408038286176 5.542511531954081 7.137108966920226 0.6363495924636218
user_002 Jumping 1.446035047846e12 -0.957409 -3.63983 -0.268841 -6.489468363636363 -8.189497000000001 -0.8854503636363634 0.9166319932809999 13.248362428899998 7.2275483281e-2 3.773230698680111 10.932699234859088 5.532059363636363 4.549667000000001 0.6166093636363634 5.063348652892563 5.8664919669421485 0.6679141570247933 30.603680802796763 20.69946981088901 0.38020710732404106 32.91277448823795 42.085032088373026 0.6403729603527354 5.736965616790635 6.487297749323136 0.8002330662705306
user_002 Jumping 1.44603504804e12 -0.727487 -0.191003 -0.498763 -4.897433727272727 -6.269997272727273 -0.9377052727272727 0.529237335169 3.6482146009e-2 0.24876453016900002 0.9024876793325214 8.618971209554099 4.169946727272727 6.0789942727272726 0.43894227272727265 5.221379917355372 6.031807355371901 0.6270602231404957 17.388455708292526 36.95417136785098 0.1926703187869834 34.153680448202515 42.71723581389732 0.6066162822620906 5.8441150269482645 6.535842395123778 0.7788557518963898
user_002 Jumping 1.446035048363e12 -14.29288 -18.73803 -1.41845 -7.2732934545454535 -9.192791454545455 -1.1188553636363636 204.2864186944 351.11376828089993 2.0120004025 23.609578297330934 12.381614214269916 7.019586545454547 9.545238545454543 0.29959463636363637 5.931730933884297 6.700986851239668 0.8199282727272726 49.2745952691265 91.11157888963116 8.97569461378595e-2 40.95245127848688 52.09298729431737 0.9762669956791471 6.399410228957578 7.2175471799162745 0.9880622428162849
user_002 Jumping 1.446035048622e12 0.613724 -1.64717 -0.575403 -4.855630545454546 -6.144584181818183 -0.8819659999999999 0.37665714817600005 2.7131690089 0.331088612409 1.849571509697584 8.507275707386022 5.4693545454545465 4.497414181818183 0.3065629999999999 4.759319694214875 5.8956271322314056 0.7765407685950414 29.91383914388431 20.226734322819315 9.398087296899996e-2 27.058965387570314 42.589898152646015 0.8881102471901253 5.201823275311294 6.52609363652147 0.9423960139931223
user_002 Jumping 1.446035048816e12 -13.06663 -17.89499 0.612526 -6.47553490909091 -8.617987 -0.7356520909090908 170.7368195569 320.2306671001 0.375188100676 22.166250805169465 11.374319492274104 6.59109509090909 9.277003 1.3481780909090908 4.852428669421488 5.799985107438017 0.8816839008264463 43.44253449740591 86.06278466200901 1.8175841648072808 28.73750824814298 43.85939409204076 1.0641403804571345 5.360737658955434 6.622642530896618 1.031571800921843
user_002 Jumping 1.446035049852e12 -1.07237 -1.34061 -0.767005 -5.040264909090909 -6.653200636363636 -0.3629003636363637 1.1499774169 1.7972351721000002 0.5882966700250001 1.88029499255436 8.79786931494273 3.9678949090909086 5.312590636363636 0.40410463636363636 4.169313190082645 6.042575611570248 0.658412867768595 15.74419000958955 28.22361926957858 0.16330055713058678 19.867216196014347 40.23047659035462 0.5792754519203643 4.457265551435582 6.3427499233656235 0.7611014728144758
user_002 Jumping 1.446035050176e12 -3.10335 -5.55585 0.535886 -5.6081021818181815 -8.13027490909091 -0.13994581818181817 9.6307812225 30.867469222500006 0.287173804996 6.38634670605942 10.273776829050883 2.5047521818181817 2.574424909090909 0.6758318181818181 4.204466925619835 5.875676900826446 0.6029905867768596 6.273783492322941 6.627663612547734 0.4567486464669421 22.885017149386655 40.31617521487341 0.5543265915647807 4.783828712379516 6.3495019658925544 0.7445311219584986
user_002 Jumping 1.446035050241e12 0.498763 1.53341 -0.843646 -4.667512818181818 -6.604429454545454 -0.32458000000000004 0.24876453016900002 2.3513462280999997 0.711738573316 1.81984871118041 8.785329171203369 5.166275818181818 8.137839454545453 0.519066 4.421404578512397 6.080579181818181 0.5314171652892562 26.690405829530214 66.22443098795664 0.26942951235600004 24.608855252102714 43.18926455572344 0.42367363107114875 4.960731322305484 6.571853966402741 0.6509021670505858
user_002 Jumping 1.446035050435e12 -1.76214 -1.37893 -0.498763 -4.650094727272728 -6.531272545454545 -0.303678 3.1051373796000004 1.9014479449 0.24876453016900002 2.292454984218665 8.549858401319002 2.8879547272727284 5.152342545454545 0.195085 4.284591338842975 5.999821479338842 0.4937302231404958 8.3402825067769 26.546633705701016 3.8058157225e-2 23.265654469793503 41.78307817709959 0.37553256642510663 4.8234484002416265 6.463983151053195 0.61280712008356
user_002 Sitting 1.446034565105e12 -0.842448 -0.114362 9.4262 -0.8169011666666667 -0.13990883333333332 9.432586666666667 0.7097186327039999 1.3078667044000002e-2 88.85324643999999 9.46446214740954 9.46900969429797 2.5546833333333296e-2 2.554683333333331e-2 6.386666666667651e-3 1.5754019444444416e-2 1.9905258333333332e-2 1.788266666666723e-2 6.526406933611092e-4 6.5264069336111e-4 4.0789511111123685e-5 5.1015066870412e-4 5.621592646068979e-4 4.965443152592826e-4 2.2586515196110265e-2 2.370989803029313e-2 2.2283274338823784e-2
user_002 Sitting 1.446034566399e12 -1.03405 -0.267643 9.4262 -0.7867094545454545 -0.1701008181818182 9.454069090909089 1.0692594024999997 7.163277544900001e-2 88.85324643999999 9.486524053516598 9.489156748152983 0.24734054545454542 9.754218181818183e-2 2.7869090909089067e-2 9.025852892561986e-2 4.4337586776859506e-2 3.0719338842975476e-2 6.117734542575205e-2 9.514477233851243e-3 7.766862280990708e-4 1.4356791376253942e-2 2.7250634901893316e-3 1.1639260946656965e-3 0.11981982881081887 5.2202140666732545e-2 3.4116361099415286e-2
user_002 Sitting 1.446034566788e12 -0.804128 -0.191003 9.46452 -0.7518728181818181 -0.18403545454545453 9.447101818181817 0.646621840384 3.6482146009e-2 89.5771388304 9.500539080325547 9.479688318952602 5.2255181818181895e-2 6.967545454545476e-3 1.7418181818182887e-2 8.519149586776859e-2 5.9222429752066125e-2 3.610314049586772e-2 2.7306040268512475e-3 4.8546689661157324e-5 3.0339305785127694e-4 1.3260152495296018e-2 5.334299526162284e-3 1.8755207212622213e-3 0.11515273550939213 7.30362891045423e-2 4.330728254303451e-2
user_002 Sitting 1.446034567695e12 -0.765807 -0.152682 9.46452 -0.7762582727272725 -0.14919863636363637 9.440134545454544 0.586460361249 2.3311793124000002e-2 89.5771388304 9.496678945019307 9.473291927813678 1.0451272727272531e-2 3.4833636363636455e-3 2.4385454545456042e-2 2.0585528925619823e-2 3.4836776859504134e-2 2.0901818181818334e-2 1.0922910161983061e-4 1.213382222314056e-5 5.946503933885027e-4 5.659854213441012e-4 1.7696435115822694e-3 5.758951861758233e-4 2.379044811146064e-2 4.20671310120178e-2 2.39978162793164e-2
user_002 Sitting 1.446034569184e12 -0.727487 -7.6042e-2 9.4262 -0.7449051818181818 -0.13178036363636364 9.422716363636361 0.529237335169 5.782385764e-3 88.85324643999999 9.45453680308734 9.453159226117394 1.7418181818181777e-2 5.573836363636364e-2 3.483636363638354e-3 2.1535190082644606e-2 3.547014876033058e-2 3.420297520661222e-2 3.0339305785123823e-4 3.1067651808595045e-3 1.2135722314063454e-5 6.707755637640855e-4 2.3234757058317058e-3 1.8027063873779414e-3 2.5899335199268833e-2 4.820244501922808e-2 4.245828997237102e-2
user_002 Sitting 1.446034569571e12 -0.765807 -0.114362 9.46452 -0.7483889090909092 -0.1422311818181818 9.429683636363636 0.586460361249 1.3078667044000002e-2 89.5771388304 9.496140155805042 9.460479984966504 1.7418090909090855e-2 2.7869181818181807e-2 3.4836363636364e-2 2.026850413223138e-2 2.0268504132231413e-2 1.8051570247934832e-2 3.033898909173535e-4 7.766912952148754e-4 1.213572231404984e-3 5.847311275935365e-4 7.08293521345605e-4 6.299543128475302e-4 2.418121435316135e-2 2.661378442359532e-2 2.5098890669659688e-2
user_002 Sitting 1.446034570154e12 -0.727487 -0.152682 9.46452 -0.7518725454545454 -0.14571481818181817 9.450585454545456 0.529237335169 2.3311793124000002e-2 89.5771388304 9.493665675527708 9.48163678013592 2.438554545454541e-2 6.9671818181818446e-3 1.3934545454544534e-2 2.1535272727272715e-2 1.836833057851241e-2 2.691900826446285e-2 5.946548271157003e-4 4.8541622487603674e-5 1.941715570247677e-4 5.979690609361374e-4 7.038792646326072e-4 1.302935277535681e-3 2.4453405916888906e-2 2.6530723032601414e-2 3.609619477916863e-2
user_002 Sitting 1.446034570673e12 -0.765807 -0.229323 9.38788 -0.7623234545454545 -0.16313336363636363 9.457552727272725 0.586460361249 5.2589038329e-2 88.13229089439999 9.421854397833687 9.489764290796622 3.4835454545455447e-3 6.618963636363637e-2 6.967272727272622e-2 1.4567942148760348e-2 3.768703305785125e-2 2.7552396694215112e-2 1.2135088933884925e-5 4.381067961950414e-3 4.854288925619688e-3 3.6407800337866306e-4 1.973747693268971e-3 1.5257912691209207e-3 1.9080828162809472e-2 4.4426880300882834e-2 3.9061378228640635e-2
user_002 Sitting 1.446034570931e12 -0.765807 -0.152682 9.38788 -0.7658071818181817 -0.16661690909090907 9.433167272727273 0.586460361249 2.3311793124000002e-2 88.13229089439999 9.420300581657306 9.465767541734065 1.818181817325737e-7 1.3934909090909053e-2 4.528727272727373e-2 1.6468231404958688e-2 3.1036512396694218e-2 2.7552396694215275e-2 3.3057851208539194e-14 1.9418169137189978e-4 2.050937071074471e-3 5.406048559128475e-4 1.4474946131495118e-3 1.1727520745304068e-3 2.3250910862003826e-2 3.8045953965560014e-2 3.42454679414723e-2
user_002 Sitting 1.446034571707e12 -0.765807 -0.114362 9.46452 -0.7588398181818181 -0.1701006363636364 9.450585454545454 0.586460361249 1.3078667044000002e-2 89.5771388304 9.496140155805042 9.482633327890168 6.9671818181819e-3 5.573863636363639e-2 1.393454545454631e-2 1.4568008264462806e-2 2.8819586776859505e-2 2.6602314049586958e-2 4.8541622487604446e-5 3.1067955836776894e-3 1.9417155702481723e-4 4.523384929909841e-4 1.4265323351600303e-3 1.0127811894816317e-3 2.1268250821141452e-2 3.776946299803626e-2 3.182422331309331e-2
user_002 Sitting 1.44603457378e12 -0.804128 -0.114362 9.4262 -0.748388909090909 -0.13874763636363638 9.426199999999996 0.646621840384 1.3078667044000002e-2 88.85324643999999 9.461128206901542 9.4570153963809 5.5739090909090905e-2 2.4385636363636373e-2 3.552713678800501e-15 2.5018917355371924e-2 3.325310743801653e-2 2.121851239669487e-2 3.1068462553719e-3 5.946592608595046e-4 1.2621774483536189e-29 9.057764906649138e-4 1.7641233586235911e-3 7.160076165289551e-4 3.0096120857428018e-2 4.20014685293692e-2 2.6758318641666466e-2
user_002 Sitting 1.446034574816e12 -0.727487 -0.191003 9.46452 -0.7379379999999999 -0.17706809090909092 9.44361818181818 0.529237335169 3.6482146009e-2 89.5771388304 9.494359289155746 9.474194624567115 1.0450999999999877e-2 1.3934909090909081e-2 2.0901818181819465e-2 2.6919115702479342e-2 3.261997520661157e-2 2.5968925619835336e-2 1.0922340099999743e-4 1.9418169137190054e-4 4.368860033058388e-4 1.0514057918069124e-3 1.4706621768903081e-3 1.0370526341097496e-3 3.242538807488528e-2 3.834921351071373e-2 3.220330160262686e-2
user_002 Sitting 1.44603457514e12 -0.765807 -0.152682 9.38788 -0.7483888181818181 -0.17010072727272726 9.422716363636361 0.586460361249 2.3311793124000002e-2 88.13229089439999 9.420300581657306 9.454029645400169 1.7418181818181888e-2 1.7418727272727252e-2 3.483636363636222e-2 1.678478512396695e-2 3.4203421487603296e-2 2.216859504132206e-2 3.033930578512421e-4 3.034120598016522e-4 1.2135722314048601e-3 3.011860446724273e-4 1.4496971925725014e-3 7.171108640120033e-4 1.735471246297176e-2 3.807488926540038e-2 2.6778925744174342e-2
user_002 Sitting 1.446034575204e12 -0.765807 -0.152682 9.4262 -0.7483888181818181 -0.17358436363636365 9.422716363636361 0.586460361249 2.3311793124000002e-2 88.85324643999999 9.458489234247349 9.454078824014742 1.7418181818181888e-2 2.0902363636363636e-2 3.483636363638354e-3 1.6784801652892575e-2 3.166988429752065e-2 2.1535206611570278e-2 3.033930578512421e-4 4.369088055867768e-4 1.2135722314063454e-5 3.0118662047708556e-4 1.2731764436769342e-3 7.082848841472434e-4 1.735472905225217e-2 3.568159810990722e-2 2.6613622153837748e-2
user_002 Sitting 1.446034575723e12 -0.727487 -0.114362 9.38788 -0.7553561818181816 -0.15268218181818183 9.408781818181817 0.529237335169 1.3078667044000002e-2 88.13229089439999 9.4167195400847 9.440372344700105 2.7869181818181654e-2 3.832018181818182e-2 2.090181818181769e-2 2.18519834710744e-2 2.501922314049587e-2 1.4567933884297769e-2 7.766912952148669e-4 1.4684363345785127e-3 4.368860033057645e-4 5.880397760075145e-4 9.697739425169045e-4 3.5524568955670044e-4 2.424953145954607e-2 3.114119365915354e-2 1.8847962477591587e-2
user_002 Sitting 1.446034576953e12 -0.765807 -0.114362 9.38788 -0.7588399090909091 -0.17010063636363637 9.412265454545452 0.586460361249 1.3078667044000002e-2 88.13229089439999 9.419757423771218 9.444454132222686 6.967090909090867e-3 5.5738636363636365e-2 2.438545454545249e-2 2.31188347107438e-2 3.166982644628099e-2 2.660231404958728e-2 4.854035573553661e-5 3.106795583677686e-3 5.946503933883295e-4 7.29263572803155e-4 1.7012463710616087e-3 9.421733505634972e-4 2.7004880536731782e-2 4.124616795608543e-2 3.069484240981695e-2
user_002 Sitting 1.446034577536e12 -0.804128 -0.152682 9.4262 -0.7588399090909091 -0.15964963636363635 9.419232727272727 0.646621840384 2.3311793124000002e-2 88.85324643999999 9.461668989850997 9.45117952966258 4.5288090909090806e-2 6.9676363636363425e-3 6.967272727273155e-3 2.0901909090909096e-2 2.3752537190082638e-2 2.7552396694215275e-2 2.051011178190073e-3 4.8547956495867476e-5 4.854288925620431e-5 6.465170749398939e-4 7.954640647776109e-4 1.179371559429033e-3 2.542670004030987e-2 2.820397249994424e-2 3.434197955023899e-2
user_002 Sitting 1.446034577665e12 -0.689167 -0.191003 9.38788 -0.7518726363636362 -0.15964963636363638 9.422716363636361 0.47495115388899994 3.6482146009e-2 88.13229089439999 9.415079616991987 9.454114323852655 6.270563636363624e-2 3.1353363636363624e-2 3.483636363636222e-2 2.6285743801652887e-2 2.311914049586777e-2 2.5968925619835336e-2 3.9319968317685795e-3 9.830334113140487e-4 1.2135722314048601e-3 1.0183138951352345e-3 6.961706396814426e-4 1.1473773824192664e-3 3.1911030931877374e-2 2.6385045758562604e-2 3.387295945764507e-2
user_002 Sitting 1.446034577859e12 -0.727487 -0.191003 9.46452 -0.7414216363636363 -0.16661700000000002 9.4262 0.529237335169 3.6482146009e-2 89.5771388304 9.494359289155746 9.456861389481157 1.3934636363636344e-2 2.438599999999999e-2 3.8320000000000576e-2 2.4068859504132248e-2 1.9635495867768592e-2 2.1851900826447137e-2 1.941740905867763e-4 5.946769959999995e-4 1.4684224000000442e-3 8.627511631870764e-4 4.766212811788128e-4 9.98438972201379e-4 2.937262608598483e-2 2.1831657774406706e-2 3.159808494515734e-2
user_002 Sitting 1.446034578442e12 -0.765807 -0.152682 9.46452 -0.7483888181818181 -0.15268236363636364 9.440134545454544 0.586460361249 2.3311793124000002e-2 89.5771388304 9.496678945019307 9.471073441510871 1.7418181818181888e-2 3.6363636363168084e-7 2.4385454545456042e-2 2.026844628099179e-2 2.7236148760330578e-2 2.1851900826446655e-2 3.033930578512421e-4 1.3223140495527202e-13 5.946503933885027e-4 4.523314104958706e-4 1.2158039469631855e-3 6.917361719008462e-4 2.1268084316549776e-2 3.486838033180184e-2 2.6300877778143567e-2
user_002 Sitting 1.446034579154e12 -0.804128 -0.152682 9.46452 -0.7518726363636364 -0.15964963636363638 9.412265454545452 0.646621840384 2.3311793124000002e-2 89.5771388304 9.49984591790351 9.443711677109876 5.225536363636352e-2 6.96763636363637e-3 5.225454545454866e-2 2.7869239669421522e-2 2.438591735537191e-2 2.881917355371981e-2 2.7306230287685827e-3 4.854795649586786e-5 2.730537520661492e-3 1.3680450747032306e-3 8.440077025770098e-4 1.3801626013524098e-3 3.698709335299586e-2 2.905181065918284e-2 3.715053971818458e-2
user_002 Sitting 1.446034579284e12 -0.765807 -0.152682 9.38788 -0.7449052727272728 -0.1526821818181818 9.412265454545455 0.586460361249 2.3311793124000002e-2 88.13229089439999 9.420300581657306 9.443018203023634 2.090172727272721e-2 1.8181818178808484e-7 2.4385454545456042e-2 2.6285694214876063e-2 1.83686694214876e-2 2.1218512396695356e-2 4.368822029834685e-4 3.3057851228725065e-14 5.946503933885027e-4 1.214685670752065e-3 6.244547164470323e-4 7.138011215627898e-4 3.4852340965164236e-2 2.4989091949229214e-2 2.6717056753369932e-2
user_002 Sitting 1.446034579348e12 -0.765807 -0.191003 9.4262 -0.7449052727272728 -0.1526821818181818 9.415749090909088 0.586460361249 3.6482146009e-2 88.85324643999999 9.459185427258417 9.44648964216224 2.090172727272721e-2 3.8320818181818206e-2 1.0450909090911509e-2 2.7869165289256214e-2 1.900209090909091e-2 1.868495867768726e-2 4.368822029834685e-4 1.4684851061239688e-3 1.0922150082649681e-4 1.2532990447565726e-3 6.685877251743054e-4 5.902374034561036e-4 3.5401963854517625e-2 2.5857063351709245e-2 2.4294801984294987e-2
user_002 Sitting 1.446034580061e12 -0.765807 -0.191003 9.50284 -0.7518725454545454 -0.17010063636363634 9.450585454545454 0.586460361249 3.6482146009e-2 90.30396806560002 9.535560317719039 9.482091909074576 1.3934454545454611e-2 2.0902363636363663e-2 5.2254545454546886e-2 1.9951809917355356e-2 3.1353165289256205e-2 3.008595041322418e-2 1.9416902347934065e-4 4.3690880558677796e-4 2.7305375206613065e-3 4.953656630586016e-4 1.7023433997783624e-3 1.3095547624343556e-3 2.22568116103498e-2 4.125946436611075e-2 3.6187770896179215e-2
user_002 Sitting 1.44603458019e12 -0.765807 -7.6042e-2 9.4262 -0.7518725454545454 -0.15964963636363635 9.447101818181817 0.586460361249 5.782385764e-3 88.85324643999999 9.457562539418547 9.478472836423377 1.3934454545454611e-2 8.360763636363636e-2 2.090181818181769e-2 1.9951809917355366e-2 3.7053644628099174e-2 2.9769256198347967e-2 1.9416902347934065e-4 6.990236858314049e-3 4.368860033057645e-4 4.953658933816674e-4 2.245143004018783e-3 1.2290176961683736e-3 2.2256816784564395e-2 4.738294001029044e-2 3.505734867568244e-2
user_002 Sitting 1.446034580838e12 -0.765807 -0.152682 9.46452 -0.7553560909090908 -0.1457149090909091 9.47497090909091 0.586460361249 2.3311793124000002e-2 89.5771388304 9.496678945019307 9.506230857534037 1.0450909090909177e-2 6.967090909090923e-3 1.0450909090909732e-2 1.80515454545455e-2 2.406889256198347e-2 2.248528925619892e-2 1.0922150082644809e-4 4.854035573553738e-5 1.092215008264597e-4 5.041842725206623e-4 1.2091784736033059e-3 9.785805175056312e-4 2.245404802080601e-2 3.477324364512614e-2 3.128227161677411e-2
user_002 Sitting 1.446034581161e12 -0.765807 -0.191003 9.46452 -0.7553561818181819 -0.17358436363636365 9.471487272727273 0.586460361249 3.6482146009e-2 89.5771388304 9.497372338581762 9.503232204177522 1.0450818181818144e-2 1.741863636363636e-2 6.967272727273155e-3 2.2485388429752107e-2 2.660266942148761e-2 2.438545454545491e-2 1.0921960066942071e-4 3.0340889276859486e-4 4.854288925620431e-5 8.351673273809183e-4 1.0679732755770098e-3 1.1352416601051547e-3 2.8899261709962737e-2 3.267986039714689e-2 3.369334741614663e-2
user_002 Sitting 1.446034581615e12 -0.804128 -0.191003 9.4262 -0.7658072727272728 -0.15268236363636364 9.440134545454542 0.646621840384 3.6482146009e-2 88.85324643999999 9.462364948911715 9.472572812816786 3.832072727272717e-2 3.832063636363636e-2 1.3934545454542757e-2 3.5469991735537214e-2 2.850295867768595e-2 2.470214876032967e-2 1.468478138710736e-3 1.4684711713140496e-3 1.9417155702471822e-4 2.1932858809804692e-3 1.4210125277220134e-3 8.340550972200801e-4 4.68325301577917e-2 3.7696319816687855e-2 2.8880012070982244e-2
user_002 Sitting 1.44630938451e12 -0.612526 3.25783 9.04299 -0.7170360909090908 1.0840186363636362 9.300787272727275 0.375188100676 10.613456308899998 81.7756681401 9.631423184019898 9.533097720787474 0.1045100909090908 2.1738113636363634 0.2577972727272755 8.075772727272727e-2 0.963391652892562 0.11939528925619798 1.0922359101826424e-2 4.725455844674586 6.645943382562125e-2 9.939310662012773e-3 2.527474715107689 3.001030772569517e-2 9.969609150820695e-2 1.5898033573708696 0.1732348340423922
user_002 Sitting 1.446309384769e12 -0.650847 3.2195 9.11964 -0.6438792727272727 2.3067839090909086 9.175375454545456 0.42360181740899994 10.36518025 83.1678337296 9.693122087181663 9.604403281195845 6.967727272727209e-3 0.9127160909090914 5.573545454545581e-2 9.374230578512394e-2 1.457437867768595 0.15961545454545503 4.854922334710655e-5 0.8330506626043729 3.106440893388571e-3 1.2473499554535682e-2 3.2644780912646967 3.788870107851274e-2 0.11168482240007226 1.8067866756384652 0.19465020184554843
user_002 Sitting 1.446309385093e12 -0.612526 3.25783 9.08132 -0.5672386363636363 3.229953636363636 9.070865454545457 0.375188100676 10.613456308899998 82.47037294239999 9.667420408360028 9.645607770802847 4.5287363636363764e-2 2.78763636363637e-2 1.0454545454543052e-2 9.152531404958676e-2 1.008362305785124 0.12129611570247983 2.050945305132243e-3 7.770916495867804e-4 1.0929752066110678e-4 1.0810873121814417e-2 1.7490213705410085 2.3338032219158845e-2 0.1039753486255969 1.3225057166383094 0.15276790310519694
user_002 Sitting 1.446309385158e12 -0.574206 3.25783 9.11964 -0.5707222727272727 3.2334381818181814 9.077833636363637 0.329712530436 10.613456308899998 83.1678337296 9.701082546238641 9.653528970031932 3.4837272727272772e-3 2.4391818181818348e-2 4.180636363636303e-2 7.410704132231402e-2 0.7888924132231406 9.817685950413252e-2 1.2136355710743833e-5 5.949607942148841e-4 1.747772040495817e-3 7.352153625508632e-3 1.2084774599566446 1.5525468077085118e-2 8.574470027651057e-2 1.0993077185013505 0.12460123625825355
user_002 Sitting 1.446309385223e12 -0.535886 3.2195 9.11964 -0.563755 3.229953636363636 9.08480181818182 0.287173804996 10.36518025 83.1678337296 9.686082168998775 9.658497968666374 2.7869000000000033e-2 1.0453636363636054e-2 3.483818181818066e-2 6.713966942148758e-2 0.5922235289256196 7.790785123966935e-2 7.766811610000018e-4 1.0927851322313403e-4 1.2136989123966134e-3 6.429819267251685e-3 0.7789004993965207 9.594037630428333e-3 8.018615383750292e-2 0.8825533974760511 9.794915839571228e-2
user_002 Sitting 1.446309386259e12 -0.612526 3.2195 9.19628 -0.5776896363636363 3.2229863636363634 9.157960000000001 0.375188100676 10.36518025 84.57156583839999 9.762783116974175 9.725842504903998 3.4836363636363665e-2 3.4863636363633432e-3 3.83199999999988e-2 2.2801991735537187e-2 2.8823636363636416e-2 2.7869090909089067e-2 1.2135722314049607e-3 1.2154731404956634e-5 1.468422399999908e-3 7.347628813275732e-4 1.1222698865514702e-3 9.9954221968436e-4 2.7106509943693843e-2 3.350029681288615e-2 3.1615537630797295e-2
user_002 Sitting 1.446309386843e12 -0.612526 3.18118 9.15796 -0.5707223636363636 3.1985999999999994 9.157960000000001 0.375188100676 10.1199061924 83.86823136159998 9.714078734222612 9.717365950494086 4.1803636363636376e-2 1.7419999999999547e-2 1.7763568394002505e-15 2.4068760330578517e-2 2.94548760330576e-2 2.2801983471074812e-2 1.7475440132231415e-3 3.034563999999842e-4 3.1554436208840472e-30 8.517070569496617e-4 1.2942976006010338e-3 1.0723565535687397e-3 2.918402057547352e-2 3.597634779408596e-2 3.274685562872777e-2
user_002 Sitting 1.446309387425e12 -0.574206 3.25783 9.11964 -0.595108 3.21602 9.16841090909091 0.329712530436 10.613456308899998 83.1678337296 9.701082546238641 9.734437069150347 2.0901999999999976e-2 4.18099999999999e-2 4.877090909091031e-2 2.818597520661156e-2 3.293892561983465e-2 2.6919008264462363e-2 4.36893603999999e-4 1.748076099999992e-3 2.378601573553838e-3 1.2720662864335061e-3 1.4499735449286213e-3 9.47689587978922e-4 3.566603827780016e-2 3.807851815562971e-2 3.0784567367090315e-2
user_002 Sitting 1.446309388593e12 -0.612526 3.18118 9.19628 -0.6160097272727273 3.2090499999999995 9.182345454545455 0.375188100676 10.1199061924 84.57156583839999 9.750213337741693 9.74650685570224 3.4837272727272772e-3 2.7869999999999617e-2 1.3934545454544534e-2 6.01731404958678e-3 2.5338264462809675e-2 2.786909090909133e-2 1.2136355710743833e-5 7.767368999999787e-4 1.941715570247677e-4 1.2467220551239715e-4 1.0217695564988677e-3 1.0833890283997167e-3 1.1165670849187573e-2 3.196513032194406e-2 3.291487548813935e-2
user_002 Sitting 1.446309389175e12 -0.612526 3.2195 9.11964 -0.6020752727272728 3.1811800000000003 9.168410909090909 0.375188100676 10.36518025 83.1678337296 9.690624442226413 9.723441354894987 1.0450727272727223e-2 3.831999999999969e-2 4.877090909090853e-2 2.6919157024793396e-2 3.420330578512377e-2 2.7235702479339062e-2 1.0921770052892458e-4 1.4684223999999761e-3 2.3786015735536644e-3 1.1308444474380178e-3 1.8865733498121553e-3 1.3283099696468977e-3 3.3628030680341925e-2 4.343470213794674e-2 3.644598701704891e-2
user_002 Sitting 1.446309389241e12 -0.574206 3.18118 9.15796 -0.5985916363636363 3.1811800000000003 9.16841090909091 0.329712530436 10.1199061924 83.86823136159998 9.711737747923179 9.723228537958677 2.438563636363633e-2 4.440892098500626e-16 1.0450909090911509e-2 2.8819330578512402e-2 3.1036198347107306e-2 2.6285619834711064e-2 5.946592608595026e-4 1.9721522630525295e-31 1.0922150082649681e-4 1.183801075178814e-3 1.7762370850488212e-3 1.298522287603321e-3 3.4406410379154845e-2 4.214542780716339e-2 3.603501474404196e-2
user_002 Sitting 1.446309389305e12 -0.612526 3.2195 9.15796 -0.5985916363636363 3.1846636363636365 9.164927272727274 0.375188100676 10.36518025 83.86823136159998 9.726695210207627 9.72109052636467 1.3934363636363689e-2 3.4836363636363554e-2 6.967272727274931e-3 2.9769388429752075e-2 3.16695041322313e-2 2.5652231404959282e-2 1.941664899504147e-4 1.213572231404953e-3 4.854288925622906e-5 1.2003492692006024e-3 1.815949387903819e-3 1.285283317806181e-3 3.464605705128078e-2 4.261395766534504e-2 3.585084821599317e-2
user_002 Sitting 1.446309390147e12 -0.612526 3.25783 9.15796 -0.5916241818181818 3.222987272727273 9.171894545454547 0.375188100676 10.613456308899998 83.86823136159998 9.739449459347073 9.739772142778746 2.0901818181818244e-2 3.484272727272675e-2 1.3934545454548086e-2 2.216865289256201e-2 3.673975206611566e-2 2.0268429752067038e-2 4.368860033057877e-4 1.2140156438016163e-3 1.9417155702486672e-4 8.958447873020282e-4 1.9089935961682876e-3 5.251458019534503e-4 2.99306663357505e-2 4.369203126621933e-2 2.291605991337626e-2
user_002 Sitting 1.446309391184e12 -0.535886 3.2195 9.11964 -0.5602713636363637 3.1846645454545457 9.14054181818182 0.287173804996 10.36518025 83.1678337296 9.686082168998775 9.695763475510269 2.4385363636363677e-2 3.4835454545454336e-2 2.0901818181819465e-2 2.9135975206611563e-2 2.3753719008264538e-2 1.7101487603305057e-2 5.94645959677688e-4 1.2135088933884152e-3 4.368860033058388e-4 1.1341499288587528e-3 1.1419832237415408e-3 4.0820156874531394e-4 3.367714252811175e-2 3.3793242279212286e-2 2.020399883056109e-2
user_002 Sitting 1.446309391897e12 -0.497565 3.14286 9.2346 -0.5602712727272726 3.1846645454545452 9.154476363636364 0.24757092922499999 9.877568979600001 85.27783716 9.767444756374362 9.708977007952216 6.270627272727264e-2 4.180454545454504e-2 8.012363636363595e-2 3.451985123966941e-2 3.1353719008264426e-2 3.736991735537145e-2 3.932076639347097e-3 1.7476200206611222e-3 6.419797104132165e-3 1.5456712015822676e-3 1.2633272028549922e-3 1.8666947413974102e-3 3.931502513775449e-2 3.5543314460739196e-2 4.3205262890039335e-2
user_002 Sitting 1.446309393711e12 -0.535886 3.14286 9.15796 -0.556787909090909 3.1742136363636364 9.137058181818183 0.287173804996 9.877568979600001 83.86823136159998 9.697060077476884 9.688865473566398 2.0901909090909054e-2 3.1353636363636195e-2 2.0901818181815912e-2 2.7552495867768565e-2 3.452090909090896e-2 2.8502479338842302e-2 4.368898036446266e-4 9.830505132231299e-4 4.3688600330569024e-4 1.119810475468068e-3 1.5546162080390586e-3 1.0547045938392187e-3 3.3463569377280546e-2 3.9428621685763485e-2 3.2476215817721414e-2
user_002 Sitting 1.446309394034e12 -0.535886 3.18118 9.15796 -0.5637551818181818 3.1776972727272725 9.133574545454547 0.287173804996 10.1199061924 83.86823136159998 9.70954743327391 9.687111701292912 2.7869181818181876e-2 3.4827272727273595e-3 2.438545454545249e-2 2.3435454545454534e-2 3.1987190082644605e-2 1.9318347107437586e-2 7.766912952148793e-4 1.2129389256198951e-5 5.946503933883295e-4 9.510144742659655e-4 1.4509074897821133e-3 5.130100796393497e-4 3.0838522569441706e-2 3.809077959010702e-2 2.264972581819369e-2
user_002 Sitting 1.446309394099e12 -0.535886 3.2195 9.15796 -0.5533041818181818 3.1742127272727276 9.133574545454548 0.287173804996 10.36518025 83.86823136159998 9.722169789537517 9.685314901567818 1.7418181818181777e-2 4.52872727272724e-2 2.4385454545450713e-2 1.773486776859502e-2 2.976958677685948e-2 1.9635041322313477e-2 3.0339305785123823e-4 2.0509370710743505e-3 5.946503933882428e-4 3.949631747610809e-4 1.1959536697220099e-3 5.273522969195818e-4 1.987368045333025e-2 3.4582563087804954e-2 2.296415243198803e-2
user_002 Sitting 1.446309394812e12 -0.612526 3.2195 9.11964 -0.584657 3.1846636363636365 9.157960000000001 0.375188100676 10.36518025 83.1678337296 9.690624442226413 9.71363099500353 2.7869000000000033e-2 3.4836363636363554e-2 3.8320000000000576e-2 3.0719396694214883e-2 1.9635041322314164e-2 3.4202975206611246e-2 7.766811610000018e-4 1.213572231404953e-3 1.4684224000000442e-3 1.4485759797633376e-3 6.023731257700965e-4 1.390091828700179e-3 3.806016263448355e-2 2.454329085045639e-2 3.728393526306174e-2
user_002 Sitting 1.44630939533e12 -0.612526 3.29615 9.15796 -0.5811732727272727 3.2020827272727272 9.147509090909091 0.375188100676 10.864604822499999 83.86823136159998 9.752334299272968 9.709300457137386 3.135272727272731e-2 9.406727272727267e-2 1.0450909090907956e-2 2.311869421487606e-2 3.1670247933884295e-2 3.2619504132230824e-2 9.829935074380188e-4 8.848651798347096e-3 1.0922150082642256e-4 8.285388598106695e-4 1.5844188613072852e-3 2.3730853361382037e-3 2.8784350953437694e-2 3.980475927960481e-2 4.871432372658173e-2
user_002 Sitting 1.446309395978e12 -0.574206 3.14286 9.08132 -0.5776895454545454 3.1986000000000003 9.133574545454547 0.329712530436 9.877568979600001 82.47037294239999 9.626923415735476 9.694850453339638 3.4835454545454336e-3 5.574000000000012e-2 5.2254545454546886e-2 2.4385553719008267e-2 3.673876033057833e-2 3.0085950413222727e-2 1.2135088933884152e-5 3.1069476000000137e-3 2.7305375206613065e-3 1.0381688949256207e-3 1.9265522670923983e-3 1.245566408414738e-3 3.222062840674621e-2 4.389250809753754e-2 3.5292582909369756e-2
user_002 Sitting 1.446309396432e12 -0.535886 3.2195 9.15796 -0.574206 3.1951154545454545 9.123123636363639 0.287173804996 10.36518025 83.86823136159998 9.722169789537517 9.68355218183141 3.832000000000002e-2 2.4384545454545492e-2 3.4836363636360446e-2 2.18519173553719e-2 2.4069999999999956e-2 2.185190082644617e-2 1.4684224000000015e-3 5.946060570247952e-4 1.2135722314047363e-3 7.733775221096924e-4 8.297486394440224e-4 7.380725661908144e-4 2.780966598342548e-2 2.880535782530782e-2 2.7167490980780952e-2
user_002 Sitting 1.446309396496e12 -0.574206 3.2195 9.15796 -0.574206 3.198599090909091 9.126607272727274 0.329712530436 10.36518025 83.86823136159998 9.724357261127132 9.687983640247957 0.0 2.0900909090908915e-2 3.1352727272725645e-2 2.0901826446280993e-2 2.4069752066115665e-2 2.2801983471074164e-2 0.0 4.368480008264389e-4 9.829935074379145e-4 7.634481220187832e-4 8.297382746806869e-4 7.877187029301007e-4 2.7630564996372824e-2 2.88051779144078e-2 2.8066326851408623e-2
user_002 Sitting 1.446309398634e12 -0.574206 3.18118 9.04299 -0.5951078181818181 3.1846636363636365 9.10222 0.329712530436 10.1199061924 81.7756681401 9.603399755447859 9.66175866037553 2.0901818181818133e-2 3.4836363636365775e-3 5.9230000000001226e-2 2.9452702479338858e-2 3.135297520661163e-2 3.3571239669422166e-2 4.3688600330578305e-4 1.2135722314051077e-5 3.5081929000001454e-3 1.3647419540728778e-3 1.6471628879789681e-3 1.5226807697972043e-3 3.6942414026060584e-2 4.0585254563436805e-2 3.902154238106439e-2
user_002 Sitting 1.446309398698e12 -0.535886 3.18118 9.11964 -0.5846568181818181 3.1846636363636365 9.105703636363637 0.287173804996 10.1199061924 83.1678337296 9.673412723904423 9.664398869095395 4.8770818181818165e-2 3.4836363636365775e-3 1.393636363636297e-2 2.7869148760330597e-2 3.135289256198352e-2 3.04044628099177e-2 2.3785927061239654e-3 1.2135722314051077e-5 1.942222314049401e-4 1.182695466860256e-3 1.6471623120961733e-3 1.3241008296018342e-3 3.439033973167837e-2 4.058524746870682e-2 3.6388196294977776e-2
user_002 Sitting 1.446309400253e12 -0.574206 3.14286 9.11964 -0.5776896363636365 3.1846645454545457 9.116156363636366 0.329712530436 9.877568979600001 83.1678337296 9.663080007928942 9.673757876165139 3.4836363636364664e-3 4.180454545454548e-2 3.483636363634801e-3 7.917404958677664e-3 2.850380165289248e-2 3.0402644628099426e-2 1.2135722314050303e-5 1.7476200206611595e-3 1.21357223140387e-5 1.445261688399688e-4 1.1121892084147188e-3 1.3989178085650042e-3 1.2021903711141958e-2 3.334950087204783e-2 3.740210968067181e-2
user_002 Sitting 1.446309400383e12 -0.574206 3.14286 9.15796 -0.5776896363636365 3.1776972727272734 9.123123636363637 0.329712530436 9.877568979600001 83.86823136159998 9.699253212058956 9.67803402396883 3.4836363636364664e-3 3.4837272727273216e-2 3.483636363636222e-2 6.967305785123975e-3 2.850396694214874e-2 3.008595041322305e-2 1.2135722314050303e-5 1.2136355710744143e-3 1.2135722314048601e-3 1.323901586205852e-4 1.1673573407963887e-3 1.3757496114199747e-3 1.1506092239356731e-2 3.4166611491284714e-2 3.7091098816562106e-2
user_002 Sitting 1.446309400901e12 -0.535886 3.18118 9.11964 -0.5707223636363635 3.177696363636364 9.137058181818183 0.287173804996 10.1199061924 83.1678337296 9.673412723904423 9.690800477019932 3.4836363636363554e-2 3.4836363636356893e-3 1.7418181818182887e-2 2.4385652892562e-2 2.5019090909090904e-2 3.0085950413222727e-2 1.213572231404953e-3 1.2135722314044888e-5 3.0339305785127694e-4 1.3095801557205114e-3 9.454957610067568e-4 1.3073482674680103e-3 3.618812174900089e-2 3.0748914793968858e-2 3.6157271294554434e-2
user_002 Standing 1.446034734537e12 -1.37893 -9.46452 0.152682 -1.4590536363636366 -9.412265454545455 0.14223145454545455 1.9014479449 89.5771388304 2.3311793124000002e-2 9.565662474100996 9.526415292004481 8.012363636363662e-2 5.225454545454511e-2 1.0450545454545462e-2 5.9618691328873166e-2 4.260542568542598e-2 6.1788887987012986e-2 6.419797104132272e-3 2.730537520661121e-3 1.0921390029752082e-4 4.641813759714882e-3 2.3892717890542994e-3 5.730558008145936e-3 6.813085761763815e-2 4.888017787461804e-2 7.570044919381877e-2
user_002 Standing 1.446034735314e12 -1.41725 -9.4262 0.114362 -1.4242172727272726 -9.408781818181817 0.1491988181818182 2.0085975625 88.85324643999999 1.3078667044000002e-2 9.53283392646405 9.51766258066411 6.967272727272711e-3 1.7418181818182887e-2 3.4836818181818205e-2 3.9903471074380255e-2 3.673652892561983e-2 6.333939669421487e-2 4.854288925619812e-5 3.0339305785127694e-4 1.2136039010330595e-3 2.846378506386181e-3 1.9505415501126994e-3 7.261695278080391e-3 5.335146208292872e-2 4.41649357535217e-2 8.521558119311509e-2
user_002 Standing 1.446034736027e12 -1.41725 -9.46452 0.152682 -1.4067990909090906 -9.408781818181815 0.15616600000000003 2.0085975625 89.5771388304 2.3311793124000002e-2 9.571261577557266 9.515199605370448 1.0450909090909288e-2 5.573818181818524e-2 3.484000000000015e-3 2.2801983471074386e-2 3.420297520661222e-2 7.410701652892565e-2 1.0922150082645041e-4 3.1067449123970757e-3 1.2138256000000103e-5 7.810992180315554e-4 1.4695256474831387e-3 9.435107387730278e-3 2.7948152318741135e-2 3.833439248877095e-2 9.713448094127172e-2
user_002 Standing 1.446034736285e12 -1.37893 -9.34956 0.191003 -1.3719627272727273 -9.419232727272725 0.17358436363636362 1.9014479449 87.41427219360001 3.6482146009e-2 9.4526293847008 9.520563831918595 6.967272727272711e-3 6.967272727272444e-2 1.7418636363636386e-2 4.5287272727272725e-2 2.945256198347175e-2 3.958722314049588e-2 4.854288925619812e-5 4.8542889256194405e-3 3.0340889276859583e-4 3.873501913148003e-3 1.2720443480090616e-3 2.2782432499729535e-3 6.223746390356859e-2 3.566573072304929e-2 4.7730946460058314e-2
user_002 Standing 1.446034737451e12 -1.37893 -9.46452 0.191003 -1.3824136363636361 -9.422716363636363 0.18403536363636366 1.9014479449 89.5771388304 3.6482146009e-2 9.56635086756225 9.525611176471477 3.4836363636361334e-3 4.180363636363715e-2 6.9676363636363425e-3 4.623735537190076e-2 3.166942148760428e-2 2.7236190082644628e-2 1.2135722314047982e-5 1.7475440132232066e-3 4.8547956495867476e-5 3.252373580165281e-3 1.456286677685994e-3 1.25110982419459e-3 5.7029585130573074e-2 3.816132437017869e-2 3.5371030861350225e-2
user_002 Standing 1.446034737646e12 -1.30229 -9.38788 0.152682 -1.3824136363636361 -9.40529818181818 0.1910026363636364 1.6959592440999998 88.13229089439999 2.3311793124000002e-2 9.479006378920946 9.508497146805437 8.012363636363617e-2 1.741818181818111e-2 3.832063636363639e-2 4.3387107438016465e-2 3.0719338842975154e-2 3.166987603305785e-2 6.419797104132201e-3 3.0339305785121503e-4 1.4684711713140515e-3 3.012968876333576e-3 1.3272067221637865e-3 1.7299211320007516e-3 5.489051718041629e-2 3.643084849634697e-2 4.159232058927166e-2
user_002 Standing 1.446034738163e12 -1.37893 -9.38788 0.267643 -1.3510609090909094 -9.401814545454544 0.20842090909090913 1.9014479449 88.13229089439999 7.163277544900001e-2 9.492384927653797 9.500906714561507 2.786909090909062e-2 1.3934545454544534e-2 5.922209090909089e-2 2.9135867768595093e-2 2.881917355371868e-2 4.433765289256198e-2 7.766862280991575e-4 1.941715570247677e-4 3.507256051644626e-3 1.782847932682195e-3 1.1462741349361407e-3 2.7228712753749056e-3 4.2223783969253574e-2 3.385667046441721e-2 5.2181139077016186e-2
user_002 Standing 1.446034739847e12 -1.37893 -9.4262 0.305964 -1.3580281818181819 -9.419232727272727 0.2293230909090909 1.9014479449 88.85324643999999 9.361396929600001e-2 9.531437895417248 9.519686143429096 2.0901818181818133e-2 6.967272727273155e-3 7.664090909090912e-2 4.433719008264456e-2 4.497057851239703e-2 4.1170512396694205e-2 4.3688600330578305e-4 4.854288925620431e-5 5.8738289462809965e-3 2.848585001352366e-3 2.9280188201352667e-3 2.2418373498437265e-3 5.337213693822242e-2 5.4111170936649175e-2 4.734804483654765e-2
user_002 Standing 1.446034740883e12 -1.41725 -9.50284 0.229323 -1.399831818181818 -9.433167272727273 0.21538836363636363 2.0085975625 90.30396806560002 5.2589038329e-2 9.610679199017572 9.539154241075058 1.7418181818182e-2 6.9672727272728e-2 1.3934636363636371e-2 4.560396694214874e-2 4.497057851239719e-2 3.515331404958677e-2 3.03393057851246e-4 4.854288925619936e-3 1.9417409058677707e-4 2.7514992228399723e-3 3.0251045986476096e-3 1.8965196208602549e-3 5.2454734989703e-2 5.500095088857655e-2 4.354904844953854e-2
user_002 Standing 1.446034741272e12 -1.49389 -9.38788 0.229323 -1.4067990909090908 -9.422716363636361 0.22932300000000003 2.2317073320999996 88.13229089439999 5.2589038329e-2 9.508763708539034 9.53024742165128 8.709090909090911e-2 3.483636363636222e-2 2.7755575615628914e-17 4.6870743801652924e-2 3.135272727272775e-2 4.02205041322314e-2 7.584826446280995e-3 1.2135722314048601e-3 7.703719777548943e-34 2.989800679188584e-3 1.6140510677686065e-3 2.4305041856851994e-3 5.467906984567847e-2 4.017525442070786e-2 4.930014387083672e-2
user_002 Standing 1.446034742059e12 -1.95374 -12.4535 0.305964 -1.434669090909091 -9.70140909090909 0.22583936363636362 3.8170999876000002 155.08966225 9.361396929600001e-2 12.609535130483438 9.809795217760076 0.5190709090909091 2.75209090909091 8.01246363636364e-2 8.012446280991732e-2 0.27267537190082775 4.877147933884297e-2 0.26943460866446284 7.574004371900831 6.419957352404964e-3 2.633868512486852e-2 0.6893434999212628 3.2767264445206614e-3 0.16229197492441985 0.8302671256416593 5.724269773971752e-2
user_002 Standing 1.446034742189e12 -1.30229 -9.38788 0.229323 -1.319708181818182 -9.380912727272728 0.1248130909090909 1.6959592440999998 88.13229089439999 5.2589038329e-2 9.480550573507267 9.474632844510081 1.7418181818182e-2 6.967272727271379e-3 0.1045099090909091 6.840619834710743e-2 0.14821371900826383 9.659252066115703e-2 3.03393057851246e-4 4.8542889256179554e-5 1.0922321098190083e-2 7.480087032682192e-3 3.0882480126521214e-2 1.2423861191243425e-2 8.648749639504077e-2 0.17573411770774966 0.11146237567557685
user_002 Standing 1.446034742213e12 -1.22565 -9.46452 0.420925 -1.319708181818182 -9.370461818181816 0.1770680909090909 1.5022179224999999 89.5771388304 0.177177855625 9.552828618190793 9.465620992624615 9.405818181818204e-2 9.405818181818404e-2 0.2438569090909091 6.777256198347112e-2 0.10609289256198341 9.817609917355372e-2 8.84694156694219e-3 8.846941566942566e-3 5.9466192111371906e-2 6.401056292261465e-3 2.082176824943647e-2 1.4755099993800152e-2 8.000660155425592e-2 0.1442974991101248 0.12147057254248929
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user_003 Jogging 1.446047740875e12 -4.36792 -13.06663 -0.11556 -4.329596 -8.579669363636363 -6.678918181818164e-2 19.0787251264 170.7368195569 1.3354113599999998e-2 13.777840861212617 11.223379404090814 3.832400000000025e-2 4.486960636363637 4.877081818181836e-2 2.4715021983471073 7.860414801652894 1.935966694214876 1.468728976000019e-3 20.132815752276777 2.378592706123984e-3 10.326157866923786 69.21213340950345 4.851537168392439 3.2134339680354076 8.319382994519692 2.2026205230117237
user_003 Jogging 1.44604774094e12 -7.89339 -0.957409 -2.10822 -4.552550545454546 -8.809591090909091 -3.892009090909087e-2 62.3056056921 0.9166319932809999 4.444591568400001 8.225985002039634 11.411497501602561 3.3408394545454545 7.852182090909091 2.069299909090909 2.672604776859504 7.591539454545455 1.9856882727272724 11.16120826104757 61.65676358879346 4.282002113763645 11.224996006406185 64.19438356391187 5.030120295116148 3.3503725175577395 8.012139761880833 2.242792967510855
user_003 Jogging 1.446047741911e12 -9.92436 -19.08292 -5.13552 -4.942721545454545 -8.123307727272728 -0.7461035454545454 98.4929214096 364.15783572640004 26.373565670399998 22.113894338320424 11.071813299428175 4.981638454545455 10.959612272727274 4.389416454545454 2.4198804876033058 7.12631 1.7234634462809917 24.816721691806027 120.11310116851428 19.266976811434386 8.522939200738632 63.12595207200314 4.573635273326528 2.9194073372413505 7.945184206297745 2.1386059181921593
user_003 Jogging 1.446047741975e12 -6.62882 -9.73276 -1.64837 -5.106454272727272 -8.276588636363636 -0.8575806363636364 43.9412545924 94.72661721760001 2.7171236568999997 11.890542269673826 11.29883403289232 1.522365727272728 1.456171363636365 0.7907893636363635 2.5566939834710745 7.205801041322314 1.7798353801652893 2.317597407574622 2.1204350402745904 0.6253478176404048 8.733602295846394 63.28795014592597 4.6278361805447465 2.9552668738789722 7.9553724077459735 2.1512406142839406
user_003 Jogging 1.44604774217e12 -2.14534 -5.47921 0.191003 -4.761570909090909 -7.970025999999999 -0.8262272727272726 4.6024837156 30.021742224100002 3.6482146009e-2 5.887334548478539 10.68804051784389 2.616230909090909 2.490815999999999 1.0172302727272726 2.4186141487603305 6.995830983471072 1.7988368677685949 6.844664169682645 6.204164345855994 1.0347574277528013 7.453212085243059 59.74840323166583 4.752632291847676 2.730057157871069 7.729709129822792 2.1800532772956895
user_003 Jogging 1.44604774327e12 -2.29862 -1.18733 1.30229 -4.639641818181818 -8.698112363636362 -2.150190909090909e-2 5.2836539044 1.4097525289 1.6959592440999998 2.8964401732816785 11.391576321113966 2.3410218181818183 7.510782363636362 1.323791909090909 2.8230356198347106 7.835078702479337 1.5758826859504131 5.480383153203307 56.41185171391101 1.7524250185745534 12.127020067467846 69.08815603044107 2.9333404785628705 3.4823871219994835 8.311928538578822 1.7126997631116991
user_003 Jogging 1.446047744371e12 -5.78577 -1.45557 -0.498763 -4.413205 -8.283557454545454 -0.5022474545454546 33.475134492900004 2.1186840249000003 0.24876453016900002 5.986867548891407 11.395727898766877 1.3725650000000007 6.827987454545454 3.484454545454596e-3 2.815434545454546 7.698899520661155 1.4970256611570247 1.883934679225002 46.62141267943011 1.2141423479339196e-5 11.479412855986366 69.20795231467186 3.978002070082623 3.388128223073378 8.319131704371067 1.994492935581027
user_003 Jogging 1.446047744436e12 -5.01936 -15.48081 -0.690364 -4.824277272727273 -8.046668363636364 -1.014346 25.193974809599997 239.6554782561 0.476602452496 16.288832233103637 11.17140295338651 0.19508272727272669 7.434141636363636 0.323982 2.509188512396695 7.497797024793388 1.0501667107438017 3.805727048016506e-2 55.266461869515396 0.104964336324 10.328273272895231 65.77303908697071 1.4919414199285874 3.2137631015517045 8.110057896647268 1.2214505392886719
user_003 Jogging 1.44604774573e12 0.996927 -4.48288 -0.383802 -4.552551363636363 -9.85468909090909 -1.8017909090909088e-2 0.993863443329 20.0962130944 0.147303975204 4.6084032498179885 11.986882630018972 5.549478363636363 5.371809090909091 0.36578409090909086 2.4214637024793393 6.722205024793388 1.3785808512396693 30.79671010846813 28.856332909173553 0.13379800116219004 8.259204611238276 51.4197099762798 3.0440588920920715 2.873883193736008 7.170753794147433 1.7447231562892926
user_003 Jogging 1.44604774806e12 -2.56686 0.15388 1.07237 -4.144961818181818 -8.792171272727273 -0.7495882727272728 6.5887702596 2.3679054399999996e-2 1.1499774169 2.7861131942008384 11.509337901370538 1.5781018181818176 8.946051272727273 1.8219582727272727 2.2149777685950416 7.928504413223141 1.5635328512396696 2.4904053485487587 80.03183337426525 3.319531947559347 7.712193560506762 75.07473299134091 3.8857866139461805 2.777083643051963 8.664567674808762 1.9712398671765394
user_003 Jogging 1.446047748385e12 -6.66714 1.95493 -1.53341 -4.695380909090909 -9.356524545454546 -1.0143462727272725 44.4507557796 3.8217513049000003 2.3513462280999997 7.115044153945919 11.895361102994752 1.9717590909090905 11.311454545454545 0.5190637272727274 1.989806033057851 7.644426099173552 1.1416929338842976 3.887833912582643 127.94900393388428 0.2694271529702564 6.719062631443501 68.53222791279427 2.551984568505031 2.5921154741723025 8.278419409089773 1.5974932139151738
user_003 Jogging 1.446047749162e12 -6.93538 1.53341 -2.18486 -4.002132181818182 -8.816556454545454 -0.8506143636363636 48.0994957444 2.3513462280999997 4.7736132196000005 7.431315845265898 11.428345861594188 2.933247818181818 10.349966454545454 1.3342456363636366 1.8856133553719012 7.412287446280991 1.6506236694214877 8.603942762868396 107.1218056102162 1.7802114181554056 5.191939889264487 69.00963976674144 4.4900357652589316 2.278582868641052 8.307204088424784 2.118970449359531
user_003 Jogging 1.446047749485e12 0.881966 2.10822 -2.8363 -3.9150412727272723 -9.189308272727272 -0.27929181818181825 0.7778640251560001 4.444591568400001 8.04459769 3.64239664006489 11.629436141235779 4.797007272727273 11.297528272727273 2.5570081818181816 2.039845504132231 7.113958429752066 1.6395383305785123 23.011278774598345 127.63414507307209 6.538290841885122 6.35398911787781 63.80273434936145 4.819507974835495 2.5207120259715925 7.987661381741307 2.1953377814895583
user_003 Jogging 1.446047749744e12 -6.9737 -13.21991 -1.72501 -4.176315818181819 -8.924550090909092 -0.23400354545454552 48.63249169 174.76602040810002 2.9756595001 15.04573599390206 11.555733771422016 2.797384181818181 4.295359909090909 1.4910064545454544 1.91886694214876 7.525665933884297 1.7240961404958677 7.825358260686574 18.450116748625458 2.2231002474962063 5.411166328523052 64.81778558076684 3.8399872278514042 2.326191378309844 8.050949358974185 1.959588535343939
user_003 Jogging 1.446047749939e12 -1.95374 -4.55952 0.957409 -4.2529567272727276 -8.377614545454545 -0.40121909090909097 3.8170999876000002 20.7892226304 0.9166319932809999 5.052024803114193 10.957703308010748 2.2992167272727277 3.818094545454545 1.3586280909090909 2.076581074380165 7.216253289256199 1.5008247272727273 5.286397558970713 14.577845958029748 1.845870289407281 5.86303889239928 61.4850680841794 2.547085777173806 2.421371283467135 7.841241488704413 1.5959592028538216
user_003 Jogging 1.446047750521e12 -6.59049 -6.36057 -2.2615 -4.287792636363637 -9.022092818181818 -1.0352465454545454 43.4345584401 40.4568507249 5.114382249999999 9.4342880714445 11.590975913207851 2.302697363636363 2.661522818181818 1.2262534545454544 2.49778626446281 7.295744867768596 1.603118561983471 5.302415148497857 7.083703711702487 1.5036975347846608 8.97714823811022 64.82860298871549 3.651281482976789 2.996188952337656 8.051621140411134 1.910832667445475
user_003 Jogging 1.446047750651e12 -4.138 1.34181 -1.26517 -4.343531727272727 -8.823523727272727 -1.1815609999999999 17.123044 1.8004540760999999 1.6006551288999997 4.530359059169593 11.379730018195447 0.20553172727272706 10.165333727272728 8.360900000000004e-2 2.1814061818181822 7.551319429752066 1.3573624214876032 4.2243290915710656e-2 103.33400978682845 6.990464881000007e-3 7.960315025729009 66.70365085604918 3.264274458154972 2.821403024335412 8.167230305069717 1.806730322476205
user_003 Jogging 1.44604775091e12 -2.10702 -9.08132 -7.7239e-2 -4.172831909090909 -9.767598181818183 -0.5684371818181818 4.439533280399999 82.47037294239999 5.965863121e-3 9.322868232787643 12.052469662406963 2.065811909090909 0.6862781818181833 0.4911981818181818 1.941033305785124 6.732975190082642 1.4982938347107437 4.267578843741825 0.47097774283967153 0.2412756538214876 5.0293433435451735 58.48312244410238 4.130988480262454 2.2426197501014684 7.6474258704548665 2.032483328409474
user_003 Jumping 1.446047778488e12 0.805325 -10.92069 -1.49509 -3.045865625 -10.45605625 -2.8985725 0.6485483556249999 119.26147007610001 2.2352941081 11.051937049215626 11.40789343159099 3.8511906249999996 0.46463375000000084 1.4034825000000002 1.2694057180059524 2.5898877395833337 0.9794885 14.831669230087888 0.2158845216390633 1.9697631278062506 2.994031096828895 19.251323506625305 2.225648644605465 1.7303268757170984 4.387633018681633 1.491860799339357
user_003 Jumping 1.446047778682e12 0.1922 -0.650847 -7.7239e-2 -2.7480122727272724 -7.510182272727272 -2.1639553636363638 3.694084e-2 0.42360181740899994 5.965863121e-3 0.6830142901360117 9.06147948144217 2.9402122727272726 6.8593352727272725 2.0867163636363637 1.4732926126361015 4.2381636859044995 1.2864592148760332 8.644848208696073 47.05048038368052 4.354385182267769 3.4053383334628764 34.89465889164739 3.5019785473636813 1.8453558826044576 5.907170125504038 1.8713574077026764
user_003 Jumping 1.446047779653e12 0.422122 -0.114362 0.344284 -2.6922735454545452 -7.0398891818181815 -1.9375156363636363 0.178186982884 1.3078667044000002e-2 0.11853147265599999 0.5565942171672286 8.651382373881274 3.114395545454545 6.925527181818182 2.2817996363636364 1.8491923636363636 5.632452041322314 1.3953661900826448 9.699459613547113 47.96292674610248 5.206609580509223 4.305371535261241 45.7487659233511 2.6415311291557284 2.074938923260451 6.76378340304826 1.6252787850568062
user_003 Jumping 1.446047779912e12 -2.68182 -13.21991 -3.18118 -2.417064454545454 -9.300787 -2.2057583636363636 7.192158512400001 174.76602040810002 10.1199061924 13.859223827938562 10.676319564800322 0.26475554545454605 3.919123000000001 0.9754216363636363 1.6018517272727266 7.413555760330579 1.5780995454545452 7.009549884893419e-2 15.359525089129006 0.951447368686314 3.8130799249221172 63.45771008430081 2.9915428584719663 1.9527109168850665 7.966034777999705 1.7296077180886902
user_003 Jumping 1.446047780042e12 -3.17999 -3.98471 -0.728685 -1.790004727272727 -7.712235181818182 -2.0455104545454543 10.1123364001 15.877913784100002 0.530981829225 5.1498768930358905 9.01807031839871 1.389985272727273 3.7275251818181814 1.3168254545454543 1.3507111900826445 6.500836636363636 1.3830142727272727 1.9320590583987116 13.894443981088665 1.7340292777388424 2.6131867887287834 54.22806571943482 2.498340144855037 1.6165354276132593 7.3639707848031835 1.5806138506463359
user_003 Jumping 1.44604778043e12 -1.99206 -14.44616 -3.64103 -3.058058454545454 -11.969273636363635 -3.0209360909090908 3.9683030435999997 208.6915387456 13.257099460900001 15.030533631581417 12.933403086552534 1.0659984545454542 2.476886363636366 0.6200939090909094 1.3953645371900827 4.610156082644628 1.3288589421487604 1.1363527050932967 6.134966058367779 0.3845164560916451 2.8087740605938762 33.79768905571308 2.244334618817004 1.6759397544643053 5.81357799085151 1.498110349345803
user_003 Jumping 1.446047781855e12 -0.420925 -2.18366 -2.68302 -2.2707519090909094 -7.266325909090909 -2.4008437272727274 0.177177855625 4.768370995600001 7.1985963204 3.484845071394853 8.674993386245026 1.8498269090909094 5.08266590909091 0.2821762727272725 1.6468234049586774 5.169758603305786 1.2481016942148762 3.4218595935968277 25.833492743434924 7.962344889025609e-2 3.8184564220586044 38.79461440106537 2.358978580515499 1.9540871070805939 6.228532283055565 1.5358966698692653
user_003 Jumping 1.446047782438e12 -2.49022 -8.08499 -1.80165 -1.9084485454545452 -8.353229636363638 -2.449615818181818 6.2011956484 65.36706330009999 3.2459427224999997 8.649520314502995 9.039489583394376 0.5817714545454546 0.26823963636363857 0.647965818181818 0.9282387107438016 3.432042975206612 0.7626072479338841 0.338458025323934 7.195250251649705e-2 0.4198597015320328 1.4550386777920103 22.957360296408897 1.026977631594913 1.2062498405355377 4.791383964619085 1.013399048546481
user_003 Jumping 1.446047782568e12 -5.13432 -17.1669 -4.67568 -2.7514953636363635 -10.690768181818182 -2.7840481818181813 26.361241862399996 294.70245560999996 21.861983462399998 18.518252642590227 11.4462039840676 2.3828246363636363 6.476131818181816 1.8916318181818186 0.9276052809917356 3.080826 0.7825592644628098 5.677853247661496 41.94028332646692 3.578270935557853 1.4291005865544335 20.058100503065358 1.1121690544572347 1.1954499515054713 4.478627077918562 1.054594260584247
user_003 Jumping 1.446047782762e12 -2.22198 -1.68549 0.267643 -2.765430909090909 -9.600380909090909 -2.6098642727272723 4.937195120399999 2.8408765400999996 7.163277544900001e-2 2.801732399061159 10.441885982259416 0.5434509090909092 7.914890909090909 2.8775072727272724 0.8313299173553719 3.10774579338843 1.0194480330578513 0.2953388905917357 62.64549810280992 8.280048104598345 1.2023843439890611 18.333901454164252 2.0604466668327537 1.0965328741032168 4.281810534594478 1.435425604771196
user_003 Jumping 1.446047784057e12 -2.8351 -17.62674 -5.02056 -2.277716909090909 -7.029436727272728 -2.5994132727272725 8.03779201 310.7019630276001 25.206022713599996 18.54577519952186 8.71471938018078 0.5573830909090911 10.597303272727274 2.421146727272727 1.3671798595041322 6.670267752066116 1.7636845867768598 0.3106759100313721 112.30283665415618 5.861951474983438 2.8017921626400346 55.3477277112353 5.347183548621389 1.6738554784210118 7.4396053464706915 2.312397792037821
user_003 Jumping 1.446047784122e12 -3.90807 -19.19788 -5.59536 -2.2986187272727268 -8.370647636363636 -2.8850732727272725 15.2730111249 368.55859649440004 31.308053529600002 20.37497634719854 9.99707912883897 1.6094512727272732 10.827232363636366 2.710286727272728 1.3491281157024795 7.46264358677686 1.9866386363636366 2.5903333992834394 117.22896065617472 7.345654144030713 2.7401008385699153 65.59974817695337 6.0089287608963105 1.655324994848418 8.099367146694448 2.4513116409172273
user_003 Jumping 1.446047784252e12 -1.49389 -6.7821 -2.0699 -2.1836587272727273 -8.224333090909091 -2.9861 2.2317073320999996 45.996880409999996 4.28448601 7.2465904915415225 9.761379035404877 0.6897687272727273 1.4422330909090917 0.9161999999999999 1.3491279669421488 6.997098214876034 1.8818117272727273 0.4757808971234381 2.080036288513192 0.8394224399999998 2.7227248763545298 60.791994286431425 5.7640904127899635 1.6500681429427482 7.796922103396406 2.4008520180948185
user_003 Jumping 1.44604778451e12 -0.344284 -6.51385 -2.8363 -2.0025072727272724 -7.524116727272728 -2.6516678181818185 0.11853147265599999 42.430241822499994 8.04459769 7.112901727505871 8.473331609269454 1.6582232727272723 1.010266727272728 0.18463218181818153 1.1065376033057854 4.376115950413224 1.118888867768595 2.7497044222143456 1.0206388602343484 3.408904256294204e-2 1.4812928383542754 31.90584041715783 2.048208537827977 1.2170837433612673 5.6485255082329076 1.4311563638638432
user_003 Jumping 1.446047784769e12 -2.4519 7.7239e-2 1.11069 -2.5703451818181815 -10.182152818181818 -3.1358972727272727 6.011813610000001 5.965863121e-3 1.2336322760999998 2.6928445460555275 11.327773506010578 0.11844518181818131 10.259391818181818 4.246587272727273 1.3076407190082644 4.473975008264463 1.5087420743801652 1.4029261095942028e-2 105.25512047897604 18.033503464889254 2.3490630347849053 33.81312160041558 5.189621264439421 1.5326653368511032 5.814905123939305 2.2780740252325913
user_003 Jumping 1.446047785029e12 -2.29862 -4.3296 -4.63736 -2.2672662727272725 -6.458115181818181 -2.658635181818182 5.2836539044 18.74543616 21.505107769600002 6.747903217592855 8.19639577552533 3.135372727272756e-2 2.128515181818181 1.978724818181818 1.3332932148760328 5.2077616859504126 1.635421950413223 9.8305621389258e-4 4.530576879230485 3.915351906088669 2.570783017457629 39.53504755990894 5.427567003101221 1.6033661520244304 6.287690160934216 2.329713931602166
user_003 Jumping 1.446047785352e12 -2.49022 -6.51385 -2.95126 -1.8840638181818186 -7.443992454545455 -2.324203363636364 6.2011956484 42.430241822499994 8.7099355876 7.572408669538379 8.94181821018264 0.6061561818181813 0.9301424545454555 0.6270566363636361 1.1328244958677687 6.097996702479341 1.6145197190082643 0.36742531675639606 0.8651649857478448 0.39320002520767733 1.9553144765137291 51.86153301692632 3.6813627580764487 1.3983255974606663 7.201495193147484 1.9186877698251086
user_003 Jumping 1.446047785611e12 -2.87342 -6.62882 -2.56806 -2.329972272727272 -8.562249818181819 -2.6934724545454545 8.2565424964 43.9412545924 6.5949321636 7.667641700836053 9.605136865433074 0.5434477272727278 1.9334298181818186 0.12541245454545447 0.882950173553719 3.814612991735537 0.9903100000000002 0.29533543227789316 3.7381508618345802 1.572828375511568e-2 1.1643291610345898 29.13604241271818 1.4706730612943126 1.0790408523473938 5.397781249061338 1.2127130993331905
user_003 Jumping 1.446047786324e12 -0.574206 -13.29655 -3.94759 -2.2428808181818183 -9.328656272727272 -3.2055689090909087 0.329712530436 176.7982419025 15.583466808099999 13.882053927320554 11.040555029331307 1.6686748181818183 3.9678937272727275 0.7420210909090912 1.6753259338842974 7.225121256198347 2.124083900826447 2.7844756488341242 15.744180630930257 0.5505952993539177 3.39283596636857 57.272907306964505 6.280795804892235 1.841965245700518 7.567886581269867 2.5061515925602413
user_003 Jumping 1.446047786518e12 -2.18366 -8.04667 -3.06622 -1.6576244545454544 -6.674103545454545 -2.4635480000000003 4.768370995600001 64.7488980889 9.4017050884 8.883635189093482 8.263893722958313 0.5260355454545458 1.3725664545454554 0.6026719999999997 1.5052596115702483 5.776549446280992 1.707310859504132 0.2767133950816615 1.8839386721434819 0.3632135395839996 2.8409857953691744 45.87364227916548 4.382206722332543 1.6855224102245494 6.7730083625495014 2.0933720936165514
user_003 Jumping 1.446047786906e12 -4.44456 -19.4278 -8.62267 -2.946580545454546 -11.077455454545456 -3.81521 19.7541135936 377.43941284000005 74.35043792889999 21.715063075259533 12.256086381514585 1.4979794545454541 8.350344545454545 4.807459999999999 1.266154644628099 3.991645636363637 1.7177616033057852 2.2439424462402964 69.72825402780248 23.11167165159999 2.4407635313636784 27.42025693095353 5.242709314360911 1.562294316498552 5.236435517692692 2.289696336713869
user_003 Jumping 1.446047787035e12 -2.91174 3.41111 -1.53341 -2.8211684545454547 -8.597085454545455 -3.1115099999999996 8.4782298276 11.635671432099999 2.3513462280999997 4.739751838208409 10.334117729844163 9.057154545454527e-2 12.008195454545454 1.5780999999999996 1.1961645867768596 3.850399669421488 1.6066013223140494 8.20320484602476e-3 144.1967580745661 2.490399609999999 2.4730005861850963 28.657848934640707 4.375157915209365 1.572577688441845 5.353302619378126 2.091687814949775
user_003 Jumping 1.446047789495e12 -3.90807 -17.74171 -7.58802 -2.1139846363636363 -7.62514390909091 -3.205570636363637 15.2730111249 314.7682737241 57.578047520400006 19.688050496923253 9.358800088769957 1.7940853636363636 10.116566090909092 4.382449363636363 1.1537262148760332 6.411527363636364 2.0167259669421482 3.2187422920142232 102.34490947173167 19.205862424836763 2.1654029518886837 50.06674660371802 6.36506042608091 1.4715308192113015 7.0757859354080255 2.5229071378235286
user_003 Jumping 1.446047790337e12 1.15021 -0.919089 1.64717 -2.354358727272727 -7.262841727272728 -2.5785121818181818 1.3229830441 0.8447245899210001 2.7131690089 2.2092706133294313 8.77086651951292 3.504568727272727 6.343752727272728 4.225682181818182 1.2636208429752065 4.4613078512396696 1.713963090909091 12.282001964177981 40.243198664780174 17.856389901735668 2.7066131737958865 32.5271555808163 4.812581558122925 1.6451787665162367 5.703258330184273 2.1937596855906816
user_003 Jumping 1.446047791438e12 -1.30229 1.34181 -1.11189 -2.3439073636363634 -6.2386457272727265 -2.9199100000000002 1.6959592440999998 1.8004540760999999 1.2362993721000002 2.1754798763261407 7.901043770785439 1.0416173636363635 7.580455727272726 1.8080200000000002 1.4647219256198347 5.322090123966942 1.7671677933884298 1.0849667322287682 57.463309033141876 3.268936320400001 3.8035068719434904 39.625116056193036 5.134791706958699 1.9502581552049694 6.294848374360818 2.2660078788386193
user_003 Jumping 1.446047791697e12 -4.59784 -13.37319 -5.02056 -2.4658354545454544 -8.840942818181817 -3.6828327272727277 21.140132665599996 178.8422107761 25.206022713599996 15.006277558252078 10.518982065674521 2.1320045454545453 4.532247181818182 1.337727272727272 1.5153941652892562 7.493047033057851 2.419879297520661 4.545443381838842 20.54126451709885 1.789514256198345 3.95029581043249 61.87828044261103 7.525001145120626 1.987535109232662 7.866274877132824 2.743173553590918
user_003 Jumping 1.446047792085e12 -4.02303 -4.06135 -7.7413 -2.4031294545454545 -8.133757090909093 -3.9092709090909095 16.1847703809 16.4945638225 59.927725689999995 9.623256200133092 9.876822030790589 1.6199005454545459 4.072407090909093 3.8320290909090904 0.9177882479338845 4.391951958677687 1.5714489669421488 2.624077777163935 16.58449951408666 14.68444695357355 1.2166755875009239 31.272381047682792 4.2373374635131755 1.1030301843108936 5.592171407215876 2.0584794056568008
user_003 Jumping 1.446047794093e12 -2.10702 -5.93905 -2.14654 -2.065214 -6.7124228181818175 -2.940811181818182 4.439533280399999 35.2723149025 4.607633971599999 6.657287897822957 8.3093839032925 4.180599999999979e-2 0.7733728181818176 0.794271181818182 0.9722588347107437 5.3952462231404965 1.9115816198347106 1.7477416359999822e-3 0.5981055159024866 0.6308667102668516 1.4342084263393786 40.828681700373515 5.156018342640205 1.1975844130329096 6.389732521817601 2.2706867557283643
user_003 Jumping 1.446047794805e12 -1.99206 -18.35483 -5.78697 -2.0582473636363634 -7.384770727272726 -3.097577727272727 3.9683030435999997 336.8997843289 33.4890217809 19.34831024026129 9.33222617185624 6.618736363636346e-2 10.970059272727273 2.689392272727273 1.305741933884297 6.121432487603307 2.2140271570247934 4.380767105132208e-3 120.34220044714962 7.232830796605167 2.3505269335475982 54.14035826919018 5.733336804386699 1.5331428288152407 7.358013201210649 2.3944387242914984
user_003 Sitting 1.446047527495e12 0.422122 -0.689167 9.4262 0.453475 -0.6612976363636364 9.440134545454544 0.178186982884 0.47495115388899994 88.85324643999999 9.460781393562215 9.474509020745439 3.135300000000002e-2 2.786936363636361e-2 1.3934545454544534e-2 3.3399114128295944e-2 4.658829602518689e-2 2.430351620097068e-2 9.830106090000013e-4 7.767014294958663e-4 1.941715570247677e-4 2.3041740084988873e-3 3.977240666965758e-3 8.163654980999173e-4 4.8001812554307646e-2 6.306536820605868e-2 2.857211049432501e-2
user_003 Sitting 1.446047528855e12 0.460442 -0.612526 9.46452 0.45695854545454556 -0.6612977272727272 9.447101818181817 0.21200683536400003 0.375188100676 89.5771388304 9.495490180419335 9.481359853221797 3.4834545454544563e-3 4.877172727272716e-2 1.7418181818182887e-2 2.5969123966942145e-2 3.040279338842974e-2 1.8368264462810237e-2 1.2134455570247312e-5 2.3786813811652783e-3 3.0339305785127694e-4 1.1694653645424491e-3 1.2224157735432e-3 6.9504591435009e-4 3.419744675472789e-2 3.496306298857696e-2 2.6363723453831214e-2
user_003 Sitting 1.446047528985e12 0.422122 -0.689167 9.4262 0.4604421818181818 -0.657814 9.436650909090908 0.178186982884 0.47495115388899994 88.85324643999999 9.460781393562215 9.470900946809623 3.832018181818181e-2 3.1352999999999964e-2 1.0450909090907956e-2 2.343555371900825e-2 3.578669421487602e-2 2.3752066115702807e-2 1.4684363345785116e-3 9.830106089999977e-4 1.0922150082642256e-4 1.1032685002223886e-3 1.7707423253027798e-3 9.521025779113177e-4 3.321548584956102e-2 4.2080189226080957e-2 3.0856159480909442e-2
user_003 Sitting 1.446047529664e12 0.537083 -0.804128 9.4262 0.4883118181818181 -0.6996179090909092 9.443618181818183 0.28845814888899995 0.646621840384 88.85324643999999 9.475670236414572 9.48224125108708 4.877118181818185e-2 0.1045100909090908 1.7418181818182887e-2 3.0719801652892575e-2 4.1487272727272664e-2 2.660231404958728e-2 2.378628175942152e-3 1.0922359101826424e-2 3.0339305785127694e-4 1.0690789414845984e-3 2.3245799321532615e-3 1.1959202716754786e-3 3.269677264631172e-2 4.821389770754136e-2 3.458208021035575e-2
user_003 Sitting 1.446047530053e12 0.422122 -0.765807 9.38788 0.4848279999999999 -0.7065851818181818 9.464519999999998 0.178186982884 0.586460361249 88.13229089439999 9.428517287385805 9.504046308773319 6.270599999999993e-2 5.9221818181818264e-2 7.663999999999938e-2 7.442383471074378e-2 7.664065289256196e-2 6.618909090909061e-2 3.932042435999991e-3 3.5072237487603405e-3 5.8736895999999044e-3 8.341804448644628e-3 8.0692826851728e-3 5.415841894515349e-3 9.133347934161179e-2 8.982918615446095e-2 7.359240378269587e-2
user_003 Sitting 1.446047530061e12 0.345482 -0.689167 9.34956 0.47437709090909086 -0.7100688181818182 9.447101818181817 0.119357812324 0.47495115388899994 87.41427219360001 9.381288885852147 9.48648976812681 0.12889509090909085 2.0901818181818244e-2 9.754181818181706e-2 8.297463636363635e-2 7.790738016528924e-2 6.998942148760308e-2 1.6613944460462795e-2 4.368860033057877e-4 9.514406294214657e-3 9.741838863456797e-3 8.104585913635609e-3 5.998356565589729e-3 9.870075411797417e-2 9.002547369292543e-2 7.744905787412606e-2
user_003 Sitting 1.446047530126e12 0.268841 -0.804128 9.31124 0.3594163636363637 -0.6961341818181818 9.433167272727271 7.2275483281e-2 0.646621840384 86.6991903376 9.349764043079643 9.466339542582668 9.05753636363637e-2 0.10799381818181819 0.12192727272727133 8.899164462809915e-2 7.062327272727278e-2 7.88568595041319e-2 8.203896497859516e-3 1.1662664765487605e-2 1.4866259834710403e-2 9.601687393040568e-3 6.715567793308799e-3 8.253394421036763e-3 9.798820027452575e-2 8.19485679759494e-2 9.08481943741138e-2
user_003 Sitting 1.446047530198e12 0.422122 -0.535886 9.57948 0.43257318181818183 -0.6403957272727271 9.44361818181818 0.178186982884 0.287173804996 91.7664370704 9.603738743753913 9.47623788966848 1.0451181818181832e-2 0.10450972727272712 0.13586181818181942 9.057513223140498e-2 7.094005785123968e-2 5.7955041322314375e-2 1.0922720139669449e-4 1.0922283094619801e-2 1.8458433639669758e-2 1.2908162652194589e-2 7.0321907231382375e-3 4.926000012021046e-3 0.11361409530597244 8.385815835765914e-2 7.018546866710407e-2
user_003 Sitting 1.446047530263e12 0.537083 -0.612526 9.46452 0.4569586363636363 -0.6334282727272726 9.454069090909092 0.28845814888899995 0.375188100676 89.5771388304 9.499514991828004 9.48705168646079 8.012436363636366e-2 2.090227272727263e-2 1.0450909090907956e-2 6.460612396694213e-2 5.2888438016528934e-2 4.782082644628134e-2 6.4199136481322356e-3 4.369050051652852e-4 1.0922150082642256e-4 7.016752513570993e-3 8.101260912214124e-3 3.990446146356166e-3 8.376605824300791e-2 9.000700479526093e-2 6.316997820449335e-2
user_003 Sitting 1.446047530271e12 0.268841 -0.689167 9.46452 0.42908936363636363 -0.636911909090909 9.457552727272725 7.2275483281e-2 0.47495115388899994 89.5771388304 9.49338535336947 9.489527910755147 0.16024836363636363 5.225509090909097e-2 6.967272727274931e-3 6.428945454545452e-2 5.637208264462811e-2 4.6554049586777294e-2 2.567953804813223e-2 2.730594525917362e-3 4.854288925622906e-5 6.91415792560931e-3 8.331843666842975e-3 3.9551422268971105e-3 8.315141565607473e-2 9.127893331345943e-2 6.288992150493679e-2
user_003 Sitting 1.446047530287e12 0.268841 -0.459245 9.38788 0.42560572727272733 -0.6369118181818182 9.440134545454544 7.2275483281e-2 0.210905970025 88.13229089439999 9.402950193833103 9.472311407267723 0.15676472727272733 0.17766681818181818 5.225454545454511e-2 8.614152066115698e-2 6.999001652892563e-2 3.990347107438035e-2 2.4575179716892583e-2 3.156549828285124e-2 2.730537520661121e-3 1.000219283185424e-2 1.083956498437566e-2 2.5749796255447035e-3 0.10001096355827314 0.10411323155284183 5.074425706959068e-2
user_003 Sitting 1.446047530296e12 0.422122 -0.612526 9.4262 0.42560572727272733 -0.6334280909090909 9.440134545454544 0.178186982884 0.375188100676 88.85324643999999 9.455507470440706 9.472078704193267 3.4837272727273327e-3 2.0902090909090898e-2 1.3934545454544534e-2 8.487472727272723e-2 7.125679338842976e-2 3.89533884297522e-2 1.213635571074422e-5 4.368974043719004e-4 1.941715570247677e-4 9.97571408612321e-3 1.087486959480391e-2 2.5385724586025533e-3 9.987849661525353e-2 0.10428264282613818 5.0384248119849456e-2
user_003 Sitting 1.446047530304e12 0.383802 -0.535886 9.54116 0.411671090909091 -0.6264608181818182 9.44710181818182 0.147303975204 0.287173804996 91.0337341456 9.563901501259828 9.477932023232524 2.786909090909101e-2 9.057481818181823e-2 9.405818181818049e-2 8.075765289256197e-2 7.822404132231409e-2 4.750413223140481e-2 7.766862280991791e-4 8.20379768866943e-3 8.846941566941898e-3 9.559782529792631e-3 1.1603016042987984e-2 3.3428398737790897e-3 9.777414039403584e-2 0.10771729686075483 5.781729735796278e-2
user_003 Sitting 1.446047530384e12 0.537083 -0.650847 9.38788 0.47786063636363635 -0.6299446363636364 9.415749090909088 0.28845814888899995 0.42360181740899994 88.13229089439999 9.425728134245013 9.449721334848572 5.922236363636363e-2 2.0902363636363552e-2 2.7869090909089067e-2 8.297439669421487e-2 7.505714049586772e-2 5.953851239669383e-2 3.507288354677685e-3 4.3690880558677335e-4 7.766862280990708e-4 8.225922349926371e-3 7.0972933802133705e-3 6.396628906987173e-3 9.069687067328382e-2 8.424543536722551e-2 7.997892789345937e-2
user_003 Sitting 1.446047530595e12 0.345482 -0.689167 9.31124 0.4604424545454545 -0.6787157272727272 9.433167272727273 0.119357812324 0.47495115388899994 86.6991903376 9.343099020336508 9.469798892553213 0.1149604545454545 1.0451272727272753e-2 0.1219272727272731 7.505712396694215e-2 9.025841322314052e-2 6.270545454545452e-2 1.3215906109297512e-2 1.0922910161983526e-4 1.4866259834710837e-2 6.889889590413226e-3 1.0501938145337343e-2 5.904580529526676e-3 8.300535880540018e-2 0.10247896440410267 7.684126840133937e-2
user_003 Sitting 1.446047530619e12 0.537083 -0.535886 9.50284 0.4883117272727272 -0.6682647272727272 9.450585454545454 0.28845814888899995 0.287173804996 90.30396806560002 9.533079251715314 9.487494546010293 4.8771272727272774e-2 0.13237872727272726 5.2254545454546886e-2 6.96732066115703e-2 7.252342148760332e-2 4.972099173553766e-2 2.3786370434380213e-3 1.7524127434347104e-2 2.7305375206613065e-3 6.233436839096926e-3 6.4662058201202105e-3 3.8801213980466528e-3 7.895211738197352e-2 8.04127217554549e-2 6.2290620466059356e-2
user_003 Sitting 1.446047530715e12 0.383802 -0.689167 9.34956 0.4674097272727273 -0.6856832727272727 9.450585454545452 0.147303975204 0.47495115388899994 87.41427219360001 9.382778230497244 9.487465577278895 8.36077272727273e-2 3.4837272727272772e-3 0.10102545454545186 5.827223966942152e-2 5.668853719008264e-2 7.632330578512284e-2 6.990252059710749e-3 1.2136355710743833e-5 1.020614246611516e-2 4.847752127121718e-3 4.378841716747557e-3 8.482869897520463e-3 6.962580072876517e-2 6.617281705313412e-2 9.210249669536903e-2
user_003 Sitting 1.446047530806e12 0.498763 -0.842448 9.38788 0.453475090909091 -0.6961341818181819 9.4262 0.24876453016900002 0.7097186327039999 88.13229089439999 9.438790921366623 9.46375777907497 4.528790909090902e-2 0.1463138181818181 3.8320000000000576e-2 7.75906033057851e-2 8.835833884297518e-2 6.143867768595095e-2 2.05099470982644e-3 2.1407733390942124e-2 1.4684224000000442e-3 7.474605228604802e-3 9.941506158927872e-3 4.905038309842278e-3 8.645579927688368e-2 9.970710184800215e-2 7.003597868126266e-2
user_003 Sitting 1.446047531072e12 0.537083 -0.842448 9.50284 0.43605681818181813 -0.7031014545454546 9.433167272727273 0.28845814888899995 0.7097186327039999 90.30396806560002 9.555215583501663 9.470374211032171 0.10102618181818185 0.1393465454545454 6.9672727272728e-2 8.677482644628101e-2 7.474023966942149e-2 5.162115702479397e-2 1.0206289412760337e-2 1.9417459730115685e-2 4.854288925619936e-3 1.0827435768694223e-2 7.281530642746053e-3 3.1630105340346233e-3 0.10405496513234831 8.533188526422027e-2 5.624064841406635e-2
user_003 Sitting 1.446047531137e12 0.575403 -0.612526 9.4262 0.46044254545454544 -0.7135523636363637 9.461036363636365 0.331088612409 0.375188100676 88.85324643999999 9.463589337724086 9.499969737709781 0.11496045454545456 0.10102636363636364 3.4836363636365775e-2 9.374212396694216e-2 6.428938016528928e-2 6.618909090909159e-2 1.3215906109297524e-2 1.0206326149586777e-2 1.2135722314051078e-3 1.0754603411913602e-2 5.863855093449286e-3 6.155017708189375e-3 0.10370440401407069 7.657581271817679e-2 7.845392092298112e-2
user_003 Sitting 1.446047531291e12 0.383802 -0.727487 9.34956 0.4395404545454546 -0.6612975454545454 9.436650909090908 0.147303975204 0.529237335169 87.41427219360001 9.385670647533559 9.470928100179533 5.573845454545462e-2 6.618945454545455e-2 8.709090909090733e-2 8.139105785123965e-2 7.442380165289253e-2 5.795504132231389e-2 3.106775315115711e-3 4.381043893024794e-3 7.584826446280685e-3 9.328115414305027e-3 7.752650081687448e-3 4.160346258752776e-3 9.658216923586375e-2 8.804913447437998e-2 6.450074618756574e-2
user_003 Sitting 1.446047531299e12 0.460442 -0.612526 9.50284 0.4465077272727273 -0.6717485454545454 9.450585454545454 0.21200683536400003 0.375188100676 90.30396806560002 9.53368569870226 9.485749208759716 1.3934272727272712e-2 5.922254545454542e-2 5.2254545454546886e-2 7.790738016528921e-2 6.745647933884294e-2 5.193785123966954e-2 1.941639564380161e-4 3.507309890115698e-3 2.7305375206613065e-3 9.097534271949656e-3 6.393425574300523e-3 3.133222851990991e-3 9.538099533947869e-2 7.995889928144662e-2 5.597519854356026e-2
user_003 Sitting 1.446047531379e12 0.383802 -0.842448 9.54116 0.48831172727272726 -0.7623236363636363 9.478454545454547 0.147303975204 0.7097186327039999 91.0337341456 9.585966657229097 9.522192588486204 0.10450972727272728 8.012436363636366e-2 6.270545454545307e-2 6.2389223140495866e-2 5.700529752066119e-2 7.093950413223092e-2 1.0922283094619836e-2 6.4199136481322356e-3 3.93197402975188e-3 5.983005936812919e-3 5.2691818403899394e-3 6.601832938842907e-3 7.734989293342893e-2 7.258913031845704e-2 8.125166422198937e-2
user_003 Sitting 1.446047531436e12 0.575403 -0.650847 9.54116 0.45347509090909094 -0.710068909090909 9.488905454545455 0.331088612409 0.42360181740899994 91.0337341456 9.580627566888193 9.527012641437604 0.12192790909090906 5.9221909090909075e-2 5.225454545454511e-2 7.379029752066112e-2 7.537373553719011e-2 6.58723966942144e-2 1.4866415015280984e-2 3.507234516371899e-3 2.730537520661121e-3 7.448131895531173e-3 8.757696907326832e-3 5.891341559729494e-3 8.63025601910579e-2 9.358256732600806e-2 7.675507513988566e-2
user_003 Sitting 1.446047531461e12 0.460442 -0.689167 9.31124 0.4360566363636364 -0.6821996363636363 9.471487272727273 0.21200683536400003 0.47495115388899994 86.6991903376 9.348055858137188 9.5065762271645 2.438536363636362e-2 6.967363636363633e-3 0.16024727272727368 6.365588429752062e-2 6.84063140495868e-2 7.252297520661166e-2 5.946459596776853e-4 4.854415604132226e-5 2.567918841652923e-2 6.552275419301271e-3 7.945683151519166e-3 7.061887139293805e-3 8.094612664792103e-2 8.913856152933569e-2 8.403503518946015e-2
user_003 Sitting 1.446047531541e12 0.422122 -0.727487 9.6178 0.42908936363636363 -0.6578139090909091 9.450585454545454 0.178186982884 0.529237335169 92.50207684000002 9.654506779636804 9.483805630602435 6.967363636363633e-3 6.96730909090909e-2 0.16721454545454684 5.890554545454545e-2 5.890566942148759e-2 5.732165289256211e-2 4.854415604132226e-5 4.854339596826446e-3 2.7960704211570712e-2 5.5405918919316285e-3 5.697279233977457e-3 6.384493184673259e-3 7.44351522597464e-2 7.548032348882361e-2 7.990302362660164e-2
user_003 Sitting 1.44604753193e12 0.460442 -0.880768 9.46452 0.4534750909090908 -0.7170360909090907 9.422716363636363 0.21200683536400003 0.775752269824 89.5771388304 9.516559143702517 9.461390118682749 6.96690909090919e-3 0.1637319090909093 4.180363636363715e-2 3.0719553719008252e-2 7.727383471074388e-2 5.320462809917359e-2 4.853782228099312e-5 2.6808138054553784e-2 1.7475440132232066e-3 1.446381519275732e-3 9.485840937113464e-3 5.361782767843718e-3 3.8031322870441045e-2 9.7395281903763e-2 7.322419523520704e-2
user_003 Sitting 1.446047531939e12 0.460442 -0.612526 9.54116 0.453475090909091 -0.6961340909090908 9.433167272727273 0.21200683536400003 0.375188100676 91.0337341456 9.571882212064668 9.470200725599252 6.966909090909024e-3 8.360809090909083e-2 0.1079927272727268 3.0719553719008252e-2 7.537367768595048e-2 6.2072066115702415e-2 4.85378222809908e-5 6.990312865462796e-3 1.166242914380155e-2 1.4463815192757316e-3 9.128387370664928e-3 6.4120743717505455e-3 3.803132287044104e-2 9.554259453597086e-2 8.007542926360461e-2
user_003 Sitting 1.446047531971e12 0.537083 -0.689167 9.46452 0.4743770909090909 -0.7065851818181819 9.44710181818182 0.28845814888899995 0.47495115388899994 89.5771388304 9.504764496460604 9.486084813100682 6.270590909090906e-2 1.7418181818181888e-2 1.741818181818111e-2 5.352172727272724e-2 7.062314876033061e-2 7.790677685950423e-2 3.932031034917352e-3 3.033930578512421e-4 3.0339305785121503e-4 5.135698914038311e-3 8.434428638700983e-3 9.78801167002251e-3 7.16637908154342e-2 9.18391454593355e-2 9.893438062687061e-2
user_003 Sitting 1.446047531995e12 0.422122 -0.650847 9.38788 0.474377 -0.6717485454545454 9.447101818181817 0.178186982884 0.42360181740899994 88.13229089439999 9.419876840739107 9.484029092844334 5.2254999999999996e-2 2.0901545454545478e-2 5.9221818181818264e-2 6.333926446280991e-2 8.329109917355373e-2 7.695669421487607e-2 2.7305850249999997e-3 4.368746023884307e-4 3.5072237487603405e-3 6.096636627168289e-3 1.3573471843867018e-2 9.839864301727981e-3 7.808096200206738e-2 0.11650524384707762 9.919609015343286e-2
user_003 Sitting 1.446047532035e12 0.537083 -0.650847 9.57948 0.48482800000000004 -0.6403957272727273 9.443618181818183 0.28845814888899995 0.42360181740899994 91.7664370704 9.616574080029645 9.478619727881672 5.225499999999994e-2 1.0451272727272642e-2 0.13586181818181764 6.333933057851242e-2 8.044087603305784e-2 7.600661157024807e-2 2.7305850249999936e-3 1.0922910161983294e-4 1.8458433639669276e-2 4.435117760483097e-3 1.3700343289062356e-2 1.0200626228700162e-2 6.659667980074606e-2 0.11704846555620606 0.10099814963008066
user_003 Sitting 1.446047532043e12 0.460442 -0.612526 9.46452 0.48831163636363634 -0.6369119999999999 9.4262 0.21200683536400003 0.375188100676 89.5771388304 9.495490180419335 9.461188754571895 2.786963636363632e-2 2.4385999999999908e-2 3.8320000000000576e-2 6.080577685950414e-2 7.822407438016526e-2 6.048859504132264e-2 7.767166310413198e-4 5.946769959999955e-4 1.4684224000000442e-3 4.223291479851993e-3 1.3538169133596541e-2 6.362428235011264e-3 6.498685620840566e-2 0.11635363824821526 7.976483081541177e-2
user_003 Sitting 1.446047532206e12 0.498763 -0.727487 9.4262 0.463926 -0.6403955454545455 9.447101818181817 0.24876453016900002 0.529237335169 88.85324643999999 9.467378111459265 9.480533747276406 3.483700000000001e-2 8.709145454545453e-2 2.090181818181769e-2 4.655442148760331e-2 5.3205074380165314e-2 5.162115702479397e-2 1.2136165690000004e-3 7.584921454842972e-3 4.368860033057645e-4 3.293241529291509e-3 3.358336182575511e-3 4.283909976859568e-3 5.738677137887711e-2 5.795115341885363e-2 6.545158498355534e-2
user_003 Sitting 1.44604753231e12 0.15388 -0.459245 9.50284 0.4290894545454545 -0.7031014545454547 9.394847272727272 2.3679054399999996e-2 0.210905970025 90.30396806560002 9.515174884889138 9.432383116562805 0.27520945454545453 0.24385645454545468 0.10799272727272857 8.455802479338846e-2 0.10482652892561983 7.505652892561993e-2 7.57402438712066e-2 5.9465970423479404e-2 1.1662429143801934e-2 1.3054925718858756e-2 1.5519611574661167e-2 7.93565914590532e-3 0.11425815383970965 0.12457773306117416 8.908231668465588e-2
user_003 Sitting 1.446047532318e12 0.345482 -0.689167 9.50284 0.4360568181818181 -0.6961341818181819 9.412265454545455 0.119357812324 0.47495115388899994 90.30396806560002 9.534058791082265 9.449429714227982 9.057481818181806e-2 6.9671818181819e-3 9.057454545454569e-2 7.600719008264466e-2 9.405885950413224e-2 6.99894214876034e-2 8.2037976886694e-3 4.8541622487604446e-5 8.203748284297563e-3 1.0701660603646882e-2 1.4094201200951173e-2 6.735325884297508e-3 0.10344883084717238 0.11871900101058454 8.206903121334812e-2
user_003 Sitting 1.446047532358e12 0.575403 -0.612526 9.46452 0.4256057272727272 -0.6612975454545453 9.440134545454544 0.331088612409 0.375188100676 89.5771388304 9.501758550051933 9.473956697352563 0.14979727272727278 4.877154545454532e-2 2.4385454545456042e-2 7.98073966942149e-2 6.935655371900826e-2 7.252297520661183e-2 2.243922291652894e-2 2.37866364602478e-3 5.946503933885027e-4 1.2078515765728777e-2 9.352380409850493e-3 7.412719838918071e-3 0.10990230100288519 9.670770605205406e-2 8.609715348905601e-2
user_003 Sitting 1.446047532489e12 0.422122 -0.650847 9.57948 0.4499914545454545 -0.6787159090909092 9.509807272727274 0.178186982884 0.42360181740899994 91.7664370704 9.610838978501981 9.545113145434641 2.7869454545454475e-2 2.7868909090909222e-2 6.967272727272622e-2 7.854063636363634e-2 5.098814049586773e-2 5.890512396694237e-2 7.767064966611531e-4 7.766760939173626e-4 4.854288925619688e-3 7.005696718364385e-3 2.98873906277911e-3 4.942548724267481e-3 8.370004013358885e-2 5.4669361280145844e-2 7.030326254355114e-2
user_003 Sitting 1.446047532674e12 0.422122 -0.727487 9.34956 0.44999127272727274 -0.6578138181818182 9.433167272727271 0.178186982884 0.529237335169 87.41427219360001 9.387315724511081 9.467545225051337 2.7869272727272743e-2 6.967318181818183e-2 8.360727272727075e-2 4.845439669421489e-2 7.917409917355372e-2 5.700495867768525e-2 7.766963623471083e-4 4.854352264669423e-3 6.990176052892232e-3 3.6021380415386926e-3 1.0273590561117955e-2 4.172481981066776e-3 6.0017814368224814e-2 0.10135872217583426 6.459475196226684e-2
user_003 Sitting 1.446047532748e12 0.422122 -0.535886 9.4262 0.443024 -0.6856832727272728 9.419232727272727 0.178186982884 0.287173804996 88.85324643999999 9.450852195854086 9.45518690012993 2.0901999999999976e-2 0.14979727272727283 6.967272727273155e-3 5.510514049586778e-2 7.15733223140496e-2 6.618909090909061e-2 4.36893603999999e-4 2.243922291652896e-2 4.854288925620431e-5 4.918344246375656e-3 8.475250983612322e-3 6.439655558827918e-3 7.013090792493461e-2 9.206112634338297e-2 8.024746450092936e-2
user_003 Sitting 1.44604753278e12 0.460442 -0.535886 9.34956 0.44650763636363633 -0.6264610909090907 9.436650909090908 0.21200683536400003 0.287173804996 87.41427219360001 9.376217405433815 9.468417061610051 1.3934363636363689e-2 9.057509090909077e-2 8.709090909090733e-2 5.098812396694215e-2 6.08056611570248e-2 5.573818181818201e-2 1.941664899504147e-4 8.203847093190058e-3 7.584826446280685e-3 4.283975561659653e-3 6.140751440224645e-3 4.9668201688956e-3 6.545208599929915e-2 7.836294685771232e-2 7.047567075874908e-2
user_003 Sitting 1.446047532812e12 0.460442 -0.727487 9.38788 0.4116710000000001 -0.636912 9.450585454545456 0.21200683536400003 0.529237335169 88.13229089439999 9.427276121178004 9.48151896497497 4.87709999999999e-2 9.057499999999996e-2 6.270545454545662e-2 5.4155008264462796e-2 6.492275206611571e-2 6.492231404958705e-2 2.37861044099999e-3 8.203830624999993e-3 3.931974029752326e-3 5.554918965370397e-3 5.702761556047335e-3 5.493069218332115e-3 7.453132875087091e-2 7.551663098978485e-2 7.41152428204355e-2
user_003 Sitting 1.446047533573e12 0.422122 -0.612526 9.50284 0.4465077272727273 -0.678716 9.440134545454546 0.178186982884 0.375188100676 90.30396806560002 9.531911830748331 9.475293232841638 2.438572727272731e-2 6.618999999999997e-2 6.270545454545484e-2 4.3070669421487594e-2 4.2120636363636346e-2 2.7552396694215112e-2 5.946636946198365e-4 4.381116099999996e-3 3.931974029752103e-3 2.6566612249744517e-3 3.412407228598795e-3 1.1242091852742531e-3 5.1542809634074586e-2 5.8415813172451814e-2 3.352922882015411e-2
user_003 Sitting 1.446047533832e12 0.498763 -0.650847 9.46452 0.4430240909090909 -0.6682650909090909 9.450585454545454 0.24876453016900002 0.42360181740899994 89.5771388304 9.499973956699987 9.48470703154306 5.573890909090912e-2 1.7418090909090966e-2 1.393454545454631e-2 3.6103363636363635e-2 2.7235809917355372e-2 2.4068760330578375e-2 3.106825986644631e-3 3.0338989091735735e-4 1.9417155702481723e-4 1.815969944335836e-3 1.2290372737678431e-3 9.92922734785878e-4 4.261419885831289e-2 3.50576278970475e-2 3.151067652059977e-2
user_003 Sitting 1.446047534933e12 0.460442 -0.650847 9.4262 0.45695872727272724 -0.6543305454545453 9.464519999999998 0.21200683536400003 0.42360181740899994 88.85324643999999 9.459854919224343 9.498204811428216 3.4832727272727793e-3 3.4835454545453226e-3 3.83199999999988e-2 3.166985123966942e-2 1.3617900826446205e-2 1.5201322314049552e-2 1.2133188892562345e-5 1.2135088933883378e-5 1.468422399999908e-3 1.4739708828970693e-3 3.4973676497971284e-4 4.83222397595789e-4 3.8392328438075614e-2 1.8701250358725025e-2 2.1982320114032297e-2
user_003 Sitting 1.446047535192e12 0.460442 -0.650847 9.46452 0.44302390909090905 -0.6543305454545454 9.457552727272725 0.21200683536400003 0.42360181740899994 89.5771388304 9.49803913885245 9.49057392074552 1.7418090909090966e-2 3.4835454545454336e-3 6.967272727274931e-3 2.2802198347107446e-2 1.3301223140495805e-2 2.21685950413219e-2 3.0338989091735735e-4 1.2135088933884152e-5 4.854288925622906e-5 8.804058292652138e-4 3.971768098181803e-4 7.435888036062852e-4 2.967163341080524e-2 1.992929526647092e-2 2.7268824756602278e-2
user_003 Sitting 1.446047535256e12 0.460442 -0.612526 9.38788 0.43954018181818183 -0.6508468181818181 9.450585454545454 0.21200683536400003 0.375188100676 88.13229089439999 9.419102177513523 9.483221940819478 2.0901818181818188e-2 3.8320818181818095e-2 6.270545454545484e-2 2.1218677685950416e-2 1.6151553719008196e-2 2.786909090909052e-2 4.368860033057854e-4 1.4684851061239604e-3 3.931974029752103e-3 7.866259928444773e-4 5.262625810578491e-4 1.1010409881292036e-3 2.8046853528417005e-2 2.2940413707207834e-2 3.3181937678942196e-2
user_003 Sitting 1.44604753571e12 0.422122 -0.689167 9.4262 0.44302390909090905 -0.6682650909090909 9.433167272727273 0.178186982884 0.47495115388899994 88.85324643999999 9.460781393562215 9.467261238993999 2.0901909090909054e-2 2.0901909090909054e-2 6.967272727273155e-3 2.470223966942148e-2 2.1852033057851227e-2 2.818578512396722e-2 4.368898036446266e-4 4.368898036446266e-4 4.854288925620431e-5 8.627507025326816e-4 6.299638713298256e-4 1.1837845493613984e-3 2.9372618244424203e-2 2.5099081085366962e-2 3.440617022223483e-2
user_003 Sitting 1.446047537393e12 0.460442 -0.727487 9.46452 0.4604421818181818 -0.6612978181818181 9.450585454545454 0.21200683536400003 0.529237335169 89.5771388304 9.503598423804164 9.484951057799584 1.8181818178808484e-7 6.61891818181819e-2 1.393454545454631e-2 1.8051826446281e-2 1.900171900826445e-2 2.723570247933922e-2 3.3057851228725065e-14 4.381007789760341e-3 1.9417155702481723e-4 6.277611767535688e-4 7.5904256007964e-4 9.708577851239973e-4 2.5055162676653465e-2 2.7550727033594596e-2 3.1158590871924827e-2
user_003 Sitting 1.446047537522e12 0.460442 -0.650847 9.46452 0.4604421818181818 -0.6682650909090908 9.457552727272725 0.21200683536400003 0.42360181740899994 89.5771388304 9.49803913885245 9.492399032727578 1.8181818178808484e-7 1.7418090909090855e-2 6.967272727274931e-3 1.5835033057851236e-2 2.5018925619834695e-2 2.533553719008339e-2 3.3057851228725065e-14 3.033898909173535e-4 4.854288925622906e-5 6.001807958069121e-4 1.0999468960676186e-3 9.17901905935422e-4 2.449858762881877e-2 3.316544732198887e-2 3.0296895978555657e-2
user_003 Sitting 1.446047537717e12 0.460442 -0.650847 9.46452 0.4499910909090909 -0.668265 9.46452 0.21200683536400003 0.42360181740899994 89.5771388304 9.49803913885245 9.498850395313655 1.0450909090909122e-2 1.7418000000000045e-2 0.0 1.330133057851239e-2 3.293635537190081e-2 1.7418181818182565e-2 1.0922150082644693e-4 3.0338672400000155e-4 0.0 4.5233693828625117e-4 1.579867727745303e-3 5.019776048084481e-4 2.126821427121354e-2 3.974754995902644e-2 2.2404856723675967e-2
user_003 Sitting 1.446047538279e12 0.383802 -0.689167 9.4262 0.495279 -0.6787159090909091 9.48542181818182 0.147303975204 0.47495115388899994 88.85324643999999 9.45914909329021 9.523077168296753 0.11147700000000005 1.045109090909091e-2 5.922181818182004e-2 6.460606611570249e-2 4.148727272727273e-2 5.320462809917343e-2 1.2427121529000012e-2 1.0922530119008267e-4 3.507223748760551e-3 7.634576459154021e-3 2.7261733594996255e-3 4.3048716790382874e-3 8.737606342216397e-2 5.221277008069602e-2 6.561152093221348e-2
user_003 Sitting 1.446047538335e12 0.498763 -0.842448 9.50284 0.46740972727272734 -0.7135525454545454 9.481938181818181 0.24876453016900002 0.7097186327039999 90.30396806560002 9.553138292125421 9.52063797478479 3.1353272727272674e-2 0.1288954545454546 2.0901818181819465e-2 4.497107438016528e-2 5.0988008264462814e-2 4.877090909090934e-2 9.830277107107405e-4 1.661403820247935e-2 4.368860033058388e-4 3.1950531367272734e-3 4.3832547066378685e-3 3.2898839945905613e-3 5.652480107640604e-2 6.620615308744247e-2 5.735751035906773e-2
user_003 Sitting 1.446047538392e12 0.460442 -0.650847 9.46452 0.4360568181818181 -0.6856831818181818 9.436650909090908 0.21200683536400003 0.42360181740899994 89.5771388304 9.49803913885245 9.472047228613263 2.4385181818181945e-2 3.483618181818182e-2 2.786909090909262e-2 5.2888305785123955e-2 6.428925619834713e-2 6.048859504132296e-2 5.946370923057913e-4 1.2135595636694218e-3 7.766862280992689e-4 3.5889070755289252e-3 5.640976702833963e-3 4.272877502028614e-3 5.990748764160391e-2 7.510643582832274e-2 6.536725099029798e-2
user_003 Sitting 1.446047538432e12 0.422122 -0.497565 9.27292 0.40818745454545446 -0.6682648181818182 9.412265454545455 0.178186982884 0.24757092922499999 85.98704532639998 9.295848709962366 9.445277627661863 1.3934545454545533e-2 0.17069981818181817 0.139345454545456 5.003804132231404e-2 6.998995867768594e-2 6.1121983471075066e-2 1.9417155702479557e-4 2.9138427927305782e-2 1.9417155702479743e-2 3.4112903343568716e-3 7.077453178788129e-3 5.137823528775436e-3 5.840625252793464e-2 8.412760057667239e-2 7.167861277100329e-2
user_003 Sitting 1.446047538505e12 0.345482 -0.727487 9.4262 0.42212218181818173 -0.7135524545454545 9.440134545454546 0.119357812324 0.529237335169 88.85324643999999 9.460541294634941 9.477304790774603 7.664018181818172e-2 1.3934545454545533e-2 1.393454545454631e-2 6.397261983471073e-2 6.745627272727277e-2 8.582413223140571e-2 5.873717469123952e-3 1.9417155702479557e-4 1.9417155702481723e-4 7.071922085413219e-3 8.233656195504889e-3 8.81605063741558e-3 8.409472091286836e-2 9.073949633706861e-2 9.389382640736067e-2
user_003 Sitting 1.44604753857e12 0.498763 -0.689167 9.46452 0.46044245454545457 -0.6264609999999999 9.412265454545452 0.24876453016900002 0.47495115388899994 89.5771388304 9.502676176449349 9.44500141395286 3.832054545454544e-2 6.270600000000004e-2 5.225454545454866e-2 5.542180991735537e-2 7.790726446280988e-2 6.048859504132215e-2 1.4684642039338833e-3 3.932042436000005e-3 2.730537520661492e-3 4.3766354520864e-3 9.210033615250928e-3 5.885825322314023e-3 6.615614447718669e-2 9.596892004837257e-2 7.671913270048106e-2
user_003 Sitting 1.446047538748e12 0.383802 -0.689167 9.46452 0.453475 -0.6543303636363637 9.47497090909091 0.147303975204 0.47495115388899994 89.5771388304 9.49733615070526 9.50865397554464 6.967300000000004e-2 3.483663636363632e-2 1.0450909090909732e-2 4.940473553719011e-2 3.261980165289257e-2 6.2072066115702734e-2 4.854326929000005e-3 1.2135912331322283e-3 1.092215008264597e-4 3.706951965102183e-3 1.7023409238046577e-3 6.46723674590533e-3 6.0884743286821724e-2 4.125943436118166e-2 8.041913171568896e-2
user_003 Sitting 1.446047538829e12 0.307161 -0.574206 9.46452 0.4360567272727273 -0.647362909090909 9.450585454545454 9.434787992100001e-2 0.329712530436 89.5771388304 9.48689618583217 9.483547031497928 0.1288957272727273 7.3156909090909e-2 1.393454545454631e-2 7.885733884297523e-2 5.0354834710743784e-2 5.542148760330628e-2 1.6614108509165296e-2 5.351933347735523e-3 1.9417155702481723e-4 9.524480510567998e-3 3.822799975695719e-3 5.989530585725073e-3 9.759344501844372e-2 6.182879568369191e-2 7.739205763981905e-2
user_003 Sitting 1.446047538926e12 0.383802 -0.612526 9.50284 0.42908945454545455 -0.6299446363636363 9.447101818181817 0.147303975204 0.375188100676 90.30396806560002 9.53029171334645 9.478177724029353 4.5287454545454575e-2 1.7418636363636275e-2 5.573818181818346e-2 4.592104132231405e-2 4.46544297520661e-2 5.06710743801663e-2 2.050953539206614e-3 3.03408892768592e-4 3.1067449123968775e-3 2.812216471304282e-3 4.6502598296844465e-3 3.5855543200602083e-3 5.3030335387439155e-2 6.81928136219972e-2 5.987949832839457e-2
user_003 Sitting 1.44604753908e12 0.383802 -0.650847 9.31124 0.48482818181818177 -0.6369120909090908 9.422716363636363 0.147303975204 0.42360181740899994 86.6991903376 9.34184650538709 9.457423948328541 0.10102618181818179 1.3934909090909109e-2 0.11147636363636337 9.374225619834707e-2 5.003799173553718e-2 5.5421487603306445e-2 1.0206289412760326e-2 1.9418169137190133e-4 1.2426979649586719e-2 1.1577654018679938e-2 3.729024227525918e-3 4.711970000300567e-3 0.10759950752061989 6.106573693591127e-2 6.864379069005853e-2
user_003 Sitting 1.446047539104e12 0.345482 -0.765807 9.38788 0.4465079090909091 -0.6508467272727272 9.412265454545455 0.119357812324 0.586460361249 88.13229089439999 9.425397024421464 9.446224382937823 0.10102590909090908 0.11496027272727283 2.4385454545456042e-2 0.10292638842975207 5.573845454545454e-2 5.288793388429835e-2 1.0206234307644627e-2 1.3215864305528948e-2 5.946503933885027e-4 1.2494465863184822e-2 4.593966684227649e-3 4.7384479398948735e-3 0.11177864672281922 6.777880704340884e-2 6.883638529073759e-2
user_003 Sitting 1.446047539185e12 0.422122 -0.574206 9.46452 0.40470390909090903 -0.6682649090909091 9.461036363636362 0.178186982884 0.329712530436 89.5771388304 9.491313836541282 9.493686059905166 1.7418090909090966e-2 9.405890909090908e-2 3.483636363638354e-3 5.0987925619834715e-2 6.112228925619836e-2 5.288793388429818e-2 3.0338989091735735e-4 8.8470783793719e-3 1.2135722314063454e-5 4.041231345951162e-3 5.376178189951167e-3 7.048648169496783e-3 6.357067992361858e-2 7.332242624157473e-2 8.395622769930045e-2
user_003 Sitting 1.44604753925e12 0.575403 -0.650847 9.54116 0.4290894545454545 -0.6473630909090909 9.46452 0.331088612409 0.42360181740899994 91.0337341456 9.580627566888193 9.497061195942141 0.1463135454545455 3.48390909090901e-3 7.663999999999938e-2 6.618947107438017e-2 5.1938214876033055e-2 6.428892561983429e-2 2.1407653583479354e-2 1.2137622553718444e-5 5.8736895999999044e-3 7.6180346566506385e-3 5.266982370293012e-3 6.86109609737033e-3 8.728135343044721e-2 7.257397860316749e-2 8.283173363735864e-2
user_003 Sitting 1.446047539266e12 0.422122 -0.574206 9.31124 0.4290894545454545 -0.636912090909091 9.43665090909091 0.178186982884 0.329712530436 86.6991903376 9.33847363603496 9.468555330556804 6.967454545454499e-3 6.270609090909096e-2 0.12541090909090968 6.175579338842974e-2 5.542194214876033e-2 7.378975206611539e-2 4.854542284297456e-5 3.93205383709918e-3 1.5727896119008412e-2 7.3532575639436515e-3 5.581416137058603e-3 8.063635853944357e-3 8.575113739154515e-2 7.470887589208261e-2 8.979774971537069e-2
user_003 Sitting 1.446047539347e12 0.422122 -0.650847 9.34956 0.4708934545454546 -0.636912090909091 9.419232727272727 0.178186982884 0.42360181740899994 87.41427219360001 9.381687534441392 9.453234713500297 4.877145454545462e-2 1.3934909090908998e-2 6.967272727272622e-2 8.297461157024794e-2 5.320521487603303e-2 7.157289256198367e-2 2.378654778479346e-3 1.9418169137189824e-4 4.854288925619688e-3 8.887917710833963e-3 4.8455447108512375e-3 6.067861157024843e-3 9.427575356810447e-2 6.960994692464029e-2 7.789647717981117e-2
user_003 Sitting 1.446047539557e12 0.498763 -0.727487 9.50284 0.40818745454545463 -0.6752319999999999 9.443618181818183 0.24876453016900002 0.529237335169 90.30396806560002 9.543687438874873 9.477360402629962 9.057554545454538e-2 5.225500000000005e-2 5.9221818181818264e-2 7.949081818181819e-2 6.618962809917359e-2 6.967272727272751e-2 8.203929434388416e-3 2.7305850250000053e-3 3.5072237487603405e-3 1.009374481075357e-2 6.2014605697948925e-3 7.4954634001502905e-3 0.10046763066158956 7.874935282143525e-2 8.657634434503625e-2
user_003 Sitting 1.446047539711e12 0.422122 -0.727487 9.50284 0.46740972727272734 -0.6891668181818182 9.478454545454547 0.178186982884 0.529237335169 90.30396806560002 9.539989118633889 9.515677464366703 4.528772727272734e-2 3.832018181818175e-2 2.4385454545454266e-2 7.980754545454548e-2 5.067146280991737e-2 3.832000000000025e-2 2.0509782415289316e-3 1.4684363345785075e-3 5.946503933884161e-4 1.0359656993277988e-2 3.554719647222392e-3 2.4591386398197055e-3 0.10178240021377953 5.962146968351579e-2 4.9589702961599855e-2
user_003 Sitting 1.446047539776e12 0.498763 -0.612526 9.54116 0.45347509090909094 -0.6508465454545453 9.436650909090908 0.24876453016900002 0.375188100676 91.0337341456 9.573802106605557 9.470590736802814 4.528790909090907e-2 3.832054545454533e-2 0.104509090909092 5.54219917355372e-2 6.048900000000001e-2 5.827173553719059e-2 2.0509947098264446e-3 1.4684642039338746e-3 1.0922150082644855e-2 4.222202858008266e-3 7.463574826676937e-3 4.357827558226931e-3 6.497847996073983e-2 8.63919835787843e-2 6.601384368620669e-2
user_003 Sitting 1.446047539792e12 0.537083 -0.727487 9.4262 0.45695872727272735 -0.6612975454545453 9.422716363636363 0.28845814888899995 0.529237335169 88.85324643999999 9.469474215818849 9.457644533197595 8.012427272727263e-2 6.618945454545466e-2 3.4836363636365775e-3 6.017241322314049e-2 6.333923140495869e-2 5.985520661157053e-2 6.419899080074364e-3 4.381043893024809e-3 1.2135722314051077e-5 4.797001418498872e-3 7.5529355695499656e-3 4.73844793989483e-3 6.926038852402484e-2 8.690762664778026e-2 6.883638529073727e-2
user_003 Sitting 1.446047539816e12 0.345482 -0.535886 9.38788 0.4569588181818181 -0.6578139090909091 9.419232727272725 0.119357812324 0.287173804996 88.13229089439999 9.409507028092385 9.454137813344296 0.1114768181818181 0.12192790909090911 3.1352727272725645e-2 8.075757024793388e-2 6.935646280991735e-2 5.35213223140498e-2 1.242708099194213e-2 1.4866415015280998e-2 9.829935074379145e-4 7.719524672739292e-3 8.24246887406912e-3 4.164759248685209e-3 8.786082558648815e-2 9.078804367354283e-2 6.453494594934754e-2
user_003 Sitting 1.446047539873e12 0.460442 -0.497565 9.38788 0.4465078181818182 -0.6856831818181818 9.436650909090908 0.21200683536400003 0.24757092922499999 88.13229089439999 9.412325358751097 9.47302938235518 1.3934181818181846e-2 0.1881181818181818 4.877090909090853e-2 7.474023140495867e-2 8.48746694214876e-2 5.2254545454545755e-2 1.9416142294214952e-4 3.5388450330578504e-2 2.3786015735536644e-3 6.82255095679489e-3 1.0529558257280991e-2 4.3390723510142995e-3 8.259873459560316e-2 0.1026136358252693 6.587163540564557e-2
user_003 Sitting 1.446047539995e12 0.422122 -0.689167 9.27292 0.4325730909090909 -0.6682648181818182 9.440134545454546 0.178186982884 0.47495115388899994 85.98704532639998 9.308070877640166 9.474249798551595 1.045109090909091e-2 2.090218181818182e-2 0.16721454545454684 6.587278512396696e-2 5.383837190082646e-2 4.908760330578555e-2 1.0922530119008267e-4 4.3690120476033066e-4 2.7960704211570712e-2 6.992470474033807e-3 4.097512226579267e-3 4.275083996994804e-3 8.36209930222896e-2 6.401181317990662e-2 6.538412649102841e-2
user_003 Sitting 1.446047540043e12 0.537083 -0.612526 9.46452 0.44650763636363633 -0.6264608181818182 9.4262 0.28845814888899995 0.375188100676 89.5771388304 9.499514991828004 9.458218273192353 9.057536363636365e-2 1.3934818181818187e-2 3.8320000000000576e-2 5.637189256198345e-2 6.998997520661156e-2 6.302214876033073e-2 8.203896497859506e-3 1.9417915776033073e-4 1.4684224000000442e-3 5.7590313811262195e-3 6.7729492727280245e-3 5.841695422990275e-3 7.588828223860532e-2 8.229792994193733e-2 7.643098470509375e-2
user_003 Sitting 1.446047540172e12 0.498763 -0.765807 9.4262 0.45347509090909094 -0.6926505454545454 9.45406909090909 0.24876453016900002 0.586460361249 88.85324643999999 9.470399745069793 9.490850263665708 4.528790909090907e-2 7.315645454545461e-2 2.7869090909090843e-2 5.2888297520661126e-2 6.555606611570247e-2 6.3655537190083e-2 2.0509947098264446e-3 5.351866841661166e-3 7.766862280991699e-4 5.354138748736284e-3 5.332058540061606e-3 5.5967744817431225e-3 7.31719806260312e-2 7.30209458995267e-2 7.481159323088316e-2
user_003 Sitting 1.44604754018e12 0.652044 -0.727487 9.31124 0.4743770909090909 -0.6926505454545454 9.44710181818182 0.42516137793599995 0.529237335169 86.6991903376 9.36234954756043 9.485110929166572 0.17766690909090904 3.483645454545459e-2 0.13586181818181942 6.618956198347105e-2 6.080561157024793e-2 7.125619834710793e-2 3.156553058591734e-2 1.2135785652975235e-3 1.8458433639669758e-2 8.134367837546952e-3 4.75284555010293e-3 7.026583219834817e-3 9.01907303304888e-2 6.894088445982492e-2 8.382471723683187e-2
user_003 Sitting 1.44604754035e12 0.345482 -0.804128 9.34956 0.44650772727272714 -0.6647813636363636 9.408781818181819 0.119357812324 0.646621840384 87.41427219360001 9.390434060591023 9.44335301311665 0.10102572727272713 0.1393466363636363 5.9221818181818264e-2 5.478842148760328e-2 6.143899999999997e-2 8.645752066115717e-2 1.0206197570983441e-2 1.941748506585949e-2 3.5072237487603405e-3 4.3148482379737e-3 5.454524538504126e-3 1.1695526568294479e-2 6.568750442796331e-2 7.38547529851947e-2 0.10814585784159501
user_003 Sitting 1.446047540358e12 0.575403 -0.727487 9.4262 0.4569587272727272 -0.6717486363636365 9.4262 0.331088612409 0.529237335169 88.85324643999999 9.471724889774723 9.461787036578569 0.11844427272727281 5.573836363636353e-2 0.0 6.52394214876033e-2 6.4922694214876e-2 7.188958677685955e-2 1.4029045741892582e-2 3.1067651808594924e-3 0.0 5.589113015519157e-3 5.709377989187071e-3 9.361054894064549e-3 7.476037062186862e-2 7.55604260786496e-2 9.675254463870471e-2
user_003 Sitting 1.446047540383e12 0.460442 -0.650847 9.38788 0.45347490909090915 -0.6682649999999999 9.4262 0.21200683536400003 0.42360181740899994 88.13229089439999 9.421671802136444 9.461239098852479 6.967090909090867e-3 1.7417999999999934e-2 3.8320000000000576e-2 4.623757851239669e-2 5.890550413223136e-2 6.112198347107458e-2 4.854035573553661e-5 3.033867239999977e-4 1.4684224000000442e-3 3.6385488936942142e-3 5.2515310322449205e-3 7.794443468069084e-3 6.032038539079649e-2 7.246744808701988e-2 8.828614539138678e-2
user_003 Sitting 1.446047540423e12 0.575403 -0.650847 9.46452 0.47437690909090907 -0.710069 9.422716363636363 0.331088612409 0.42360181740899994 89.5771388304 9.504305827372034 9.461891292898251 0.10102609090909093 5.9222e-2 4.180363636363715e-2 6.46059090909091e-2 6.55560909090909e-2 5.257123966942132e-2 1.0206271044371905e-2 3.5072452839999997e-3 1.7475440132232066e-3 5.869341043163786e-3 6.055816182386925e-3 4.174688476033004e-3 7.661162472604133e-2 7.781912478553665e-2 6.461182922679874e-2
user_003 Sitting 1.446047540471e12 0.383802 -0.804128 9.4262 0.48831172727272726 -0.7240036363636364 9.433167272727273 0.147303975204 0.646621840384 88.85324643999999 9.46821906461759 9.474308441080531 0.10450972727272728 8.012436363636355e-2 6.967272727273155e-3 6.998997520661158e-2 8.044088429752065e-2 6.428892561983462e-2 1.0922283094619836e-2 6.419913648132217e-3 4.854288925620431e-5 6.395622050142e-3 8.861414608238164e-3 5.910096766942079e-3 7.997263313247852e-2 9.413508701986824e-2 7.687715373855929e-2
user_003 Sitting 1.446047540488e12 0.383802 -0.574206 9.2346 0.4813444545454546 -0.7205199090909091 9.419232727272727 0.147303975204 0.329712530436 85.27783716 9.260391658328496 9.45974724809149 9.754245454545463e-2 0.14631390909090913 0.18463272727272617 6.238931404958679e-2 7.664046280991733e-2 6.555570247933883e-2 9.514530438752082e-3 2.140775999346282e-2 3.4089243980164885e-2 5.660853122831709e-3 8.715779145921858e-3 7.408306848985668e-3 7.523864115487273e-2 9.335833731339616e-2 8.60715217071574e-2
user_003 Sitting 1.446047540504e12 0.460442 -0.689167 9.4262 0.48134445454545455 -0.7170362727272727 9.422716363636363 0.21200683536400003 0.47495115388899994 88.85324643999999 9.462568595748884 9.4629710671076 2.090245454545453e-2 2.7869272727272687e-2 3.4836363636365775e-3 6.555632231404962e-2 7.60070991735537e-2 6.61890909090911e-2 4.369126060247927e-4 7.766963623471052e-4 1.2135722314051077e-5 6.212486192523672e-3 8.411279385727269e-3 8.010679974755807e-3 7.881932626281242e-2 9.171302735013859e-2 8.950240206137379e-2
user_003 Sitting 1.446047540512e12 0.345482 -0.650847 9.69444 0.46044254545454544 -0.7170362727272728 9.443618181818183 0.119357812324 0.42360181740899994 93.9821669136 9.722403331652776 9.482798112951304 0.11496054545454543 6.618927272727282e-2 0.2508218181818176 6.682309090909094e-2 7.664048760330576e-2 8.519074380165295e-2 1.3215927011206606e-2 4.381019824165301e-3 6.291158447603276e-2 6.4860912804177336e-3 8.490713434833205e-3 1.3571047289556675e-2 8.053627307255863e-2 9.214506733858956e-2 0.11649483803824388
user_003 Sitting 1.44604754052e12 0.422122 -0.689167 9.65612 0.45347518181818175 -0.7065852727272728 9.457552727272727 0.178186982884 0.47495115388899994 93.24065345439999 9.689880886325332 9.495529529037851 3.135318181818175e-2 1.741827272727281e-2 0.19856727272727248 6.713976859504135e-2 7.062323966942148e-2 9.69084297520661e-2 9.830220101239627e-4 3.033962248016558e-4 3.942896179834701e-2 6.504845854223894e-3 7.882813303996995e-3 1.67141993688955e-2 8.065262459600366e-2 8.878520881316321e-2 0.12928340716772396
user_003 Sitting 1.44604754069e12 0.383802 -0.612526 9.38788 0.46392618181818174 -0.6438792727272727 9.461036363636364 0.147303975204 0.375188100676 88.13229089439999 9.415666889301043 9.495227925366775 8.012418181818176e-2 3.135327272727273e-2 7.315636363636457e-2 9.184199999999998e-2 6.840652066115696e-2 7.759008264462769e-2 6.419884512033049e-3 9.83027710710744e-4 5.351853540496005e-3 1.1899797043833205e-2 6.3106745274838375e-3 7.959930590533333e-3 0.10908619089432542 7.943975407492043e-2 8.921844310753989e-2
user_003 Sitting 1.446047540787e12 0.422122 -0.727487 9.46452 0.4604422727272727 -0.7100688181818181 9.373945454545453 0.178186982884 0.529237335169 89.5771388304 9.501818938942849 9.412453567045363 3.8320272727272675e-2 1.7418181818181888e-2 9.057454545454746e-2 3.4836586776859496e-2 6.048880165289261e-2 9.152462809917385e-2 1.4684433018925579e-3 3.033930578512421e-4 8.203748284297884e-3 1.9130624598204355e-3 5.537250364716014e-3 1.1115218392186358e-2 4.3738569476154975e-2 7.441270297950488e-2 0.10542873608360463
user_003 Sitting 1.446047540891e12 0.575403 -0.574206 9.54116 0.47437699999999994 -0.6961342727272727 9.429683636363634 0.331088612409 0.329712530436 91.0337341456 9.57572635826886 9.467791840706656 0.10102600000000006 0.12192827272727269 0.11147636363636515 4.718777685950413e-2 7.094e-2 6.048859504132215e-2 1.0206252676000012e-2 1.4866503690256189e-2 1.2426979649587114e-2 3.129960671486852e-3 6.173872703349363e-3 5.309930136138238e-3 5.5946051437852626e-2 7.857399508329306e-2 7.286926743242475e-2
user_003 Sitting 1.446047540981e12 0.383802 -0.535886 9.50284 0.4604423636363636 -0.6682649090909091 9.457552727272729 0.147303975204 0.287173804996 90.30396806560002 9.52567298650337 9.493207059307485 7.664036363636362e-2 0.1323789090909091 4.5287272727271954e-2 5.162164462809916e-2 8.582471900826447e-2 4.972099173553766e-2 5.873745338314047e-3 1.7524175572099177e-2 2.05093707107431e-3 4.04124672012096e-3 1.1492692849347104e-2 3.021794856198391e-3 6.357080084536422e-2 0.1072039777683044 5.497085460676767e-2
user_003 Sitting 1.446047541102e12 0.460442 -0.727487 9.6178 0.4395402727272728 -0.6752321818181817 9.45406909090909 0.21200683536400003 0.529237335169 92.50207684000002 9.65625812675557 9.489015016304148 2.090172727272721e-2 5.225481818181832e-2 0.16373090909091026 4.1170479338842964e-2 7.79073223140496e-2 7.410644628099257e-2 4.368822029834685e-4 2.7305660232148903e-3 2.680781059173592e-2 3.656193483053345e-3 9.832287709948916e-3 9.640176507287873e-3 6.046646577280125e-2 9.915789282729295e-2 9.81844005292484e-2
user_003 Standing 1.446047630001e12 -0.229323 -9.73276 0.382604 -0.8117916 -9.410872 0.39026859999999997 5.2589038329e-2 94.72661721760001 0.146385820816 9.742976551174953 9.459500713350298 0.5824685999999999 0.3218880000000013 7.664599999999966e-3 0.17269683666666663 0.1422949333333335 4.560130333333332e-2 0.33926966998595987 0.10361188454400083 5.874609315999948e-5 7.34666601397767e-2 3.590423294435565e-2 3.994914274266721e-3 0.27104733929661934 0.18948412319863545 6.32053342232024e-2
user_003 Standing 1.446047631037e12 -0.804128 -9.46452 0.382604 -0.7867094545454546 -9.429683636363636 0.38260436363636363 0.646621840384 89.5771388304 0.146385820816 9.506321396397242 9.47130624798105 1.7418545454545353e-2 3.4836363636364e-2 3.6363636363168084e-7 8.32913140495868e-2 7.473983471074387e-2 7.505725619834712e-2 3.034057257520626e-4 1.213572231404984e-3 1.3223140495527202e-13 1.0100381915482346e-2 6.751874596543982e-3 1.0945504611989483e-2 0.10050065629378918 8.216979126506274e-2 0.10462076568248525
user_003 Standing 1.446047631231e12 -0.727487 -9.50284 0.344284 -0.8006440909090909 -9.429683636363636 0.396539 0.529237335169 90.30396806560002 0.11853147265599999 9.536862003480234 9.472512914924552 7.315709090909095e-2 7.315636363636457e-2 5.2254999999999996e-2 6.460626446280994e-2 6.77725619834712e-2 4.845475206611569e-2 5.351959950280998e-3 5.351853540496005e-3 2.7305850249999997e-3 5.803188286028555e-3 5.375021737640885e-3 3.176314455302029e-3 7.617866030607623e-2 7.331453974240638e-2 5.635880104563997e-2
user_003 Standing 1.446047631554e12 -0.804128 -9.38788 0.267643 -0.783225909090909 -9.426199999999998 0.3826041818181818 0.646621840384 88.13229089439999 7.163277544900001e-2 9.426056731753368 9.467054139655685 2.090209090909101e-2 3.83199999999988e-2 0.11496118181818177 6.0489123966942164e-2 7.378975206611571e-2 5.985584297520662e-2 4.36897404371905e-4 1.468422399999908e-3 1.3216073325033046e-2 5.6498166748760355e-3 6.695608974906073e-3 4.943748189722764e-3 7.516526242138742e-2 8.182670086778565e-2 7.031179267891528e-2
user_003 Standing 1.446047631878e12 -0.650847 -9.50284 0.420925 -0.7867095454545456 -9.41574909090909 0.3826042727272727 0.42360181740899994 90.30396806560002 0.177177855625 9.534398131955369 9.456979008946961 0.13586254545454568 8.709090909091088e-2 3.8320727272727284e-2 6.682312396694219e-2 6.872264462809935e-2 5.573869421487603e-2 1.8458631257388492e-2 7.584826446281304e-3 1.4684781387107448e-3 6.99580428544554e-3 6.06234491960935e-3 4.234333282864011e-3 8.364092470462973e-2 7.786106163936728e-2 6.507175487770413e-2
user_003 Standing 1.446047633044e12 -0.765807 -9.46452 0.420925 -0.7449053636363636 -9.412265454545452 0.35821872727272724 0.586460361249 89.5771388304 0.177177855625 9.504776538523881 9.448962586608722 2.09016363636364e-2 5.225454545454866e-2 6.270627272727275e-2 4.877114876033059e-2 3.008595041322434e-2 6.017230578512396e-2 4.3687840267768745e-4 2.730537520661492e-3 3.9320766393471105e-3 3.7819710088888084e-3 1.1749585694967016e-3 4.582958047978211e-3 6.149773173775443e-2 3.427766867067685e-2 6.769754831586008e-2
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user_003 Walking 1.446047694407e12 -4.17632 -9.54116 1.49389 -2.7062089090909094 -9.182341818181818 0.8110947272727274 17.441648742399998 91.0337341456 2.2317073320999996 10.52174368724595 9.748098079740982 1.4701110909090902 0.35881818181818126 0.6827952727272726 1.3345601818181814 0.5314178512396698 1.4830916033057853 2.1612266196139154 0.12875048760330537 0.4662093844587106 2.2976739074978894 0.4642471196049591 2.6074609343048256 1.515808004827092 0.681356822527638 1.614763429826433
user_003 Walking 1.446047694535e12 -1.60885 -9.88604 -1.11189 -2.4832543636363638 -9.154472727272728 0.9992127272727273 2.5883983225 97.7337868816 1.2362993721000002 10.077622962593907 9.618689978504337 0.8744043636363639 0.731567272727272 2.111102727272727 1.1771632396694214 0.5098827272727274 1.5508645123966942 0.7645829911463145 0.5351906745256187 4.456754725098347 1.7062150581021485 0.38990555090390694 2.872690375200854 1.3062216726506066 0.6244241754640085 1.6949012877453524
user_003 Walking 1.446047694665e12 -2.87342 -9.31124 -1.26517 -2.444933818181818 -9.474969999999999 0.41395727272727273 8.2565424964 86.6991903376 1.6006551288999997 9.826311004792185 9.933644266781107 0.42848618181818177 0.16372999999999927 1.6791272727272726 1.1565773719008263 0.6859657024793389 1.47200647107438 0.18360040800912392 2.680751289999976e-2 2.8194683980165283 1.6581222852926367 1.0010658402313288 2.4672273237565943 1.287680971860902 1.000532778189365 1.5707410110379731
user_003 Walking 1.446047695054e12 -5.78577 -11.34221 -2.79798 -3.3855238181818184 -9.231112727272729 -1.188528090909091 33.475134492900004 128.6457276841 7.8286920804 13.036470160952312 10.174146227634331 2.400246181818182 2.111097272727271 1.609451909090909 1.5571979338842974 1.3351935537190078 1.4561710082644626 5.761181733332761 4.456731694916521 2.5903354476763716 4.214953860726055 2.375827022608414 2.522741711639002 2.053035279951627 1.5413717989532616 1.588314109878459
user_003 Walking 1.446047695377e12 -3.21831 -8.77475 1.18733 -3.3263024545454543 -8.729464545454546 -0.6555277272727272 10.357519256099998 76.99623756249999 1.4097525289 9.421438815143894 9.625389020221588 0.10799245454545447 4.528545454545352e-2 1.8428577272727273 1.2569685041322314 1.0565014049586776 1.5752488925619834 1.1662370238752051e-2 2.050772393388337e-3 3.396124602968802 3.6424844351548686 1.6223155247297527 2.8198124686093284 1.908529390697159 1.2737015053495668 1.679229724787329
user_004 Jogging 1.446046317704e12 14.94552 -16.51545 -2.33814 7.7604615 -9.75192 -2.5488999999999997 223.36856807040002 272.76008870250007 5.466898659600001 22.396329061533724 13.252263282051047 7.1850585 6.763530000000001 0.21075999999999961 3.59252925 3.3817650000000006 0.10537999999999981 51.62506564842225 45.74533806090002 4.4419777599999835e-2 25.812532824211125 22.87266903045001 2.2209888799999918e-2 5.0806035885720435 4.782537927758651 0.14902982520287647
user_004 Jogging 1.446046317963e12 -4.21464 -2.60518 5.59417 4.809798833333334 -6.028463333333332 -1.2140754999999996 17.7631903296 6.7869628323999995 31.2947379889 7.472943941372771 12.720995087782624 9.024438833333335 3.423283333333332 6.8082455 7.036142697222222 5.500772777777777 1.9598709055555552 81.44049625657472 11.71886878027777 46.35220678827025 68.62380124906085 44.288261653064815 9.080189820087265 8.28394840936741 6.654942648367814 3.0133353315034928
user_004 Jogging 1.446046318157e12 11.99486 -7.93171 10.53749 6.123333666666667 -6.1561988888888886 0.1356518888888893 143.87666641959999 62.9120235241 111.0386955001 17.827713971336873 12.839999546747189 5.871526333333332 1.7755111111111113 10.401838111111111 5.732818960185185 3.934486102292769 3.6105050307319217 34.47482148302676 3.1524397056790128 108.19823608976357 50.7951990084904 29.90219635088306 24.076787892817315 7.1270750668482785 5.468290075597952 4.906810358350659
user_004 Jogging 1.446046318221e12 18.24107 -10.26924 -5.74865 7.3351073000000016 -6.567502999999999 -0.4527782999999996 332.7366347449 105.4572901776 33.04697682249999 21.708083787957886 13.72680797086826 10.9059627 3.7017370000000005 5.2958717 6.250133334166667 3.9112111920634924 3.7790416976587293 118.94002241379128 13.702856817169003 28.046257062860892 57.60968134902049 28.28226239751165 24.47373480982167 7.590104172474874 5.318107031408042 4.947093571969472
user_004 Jogging 1.44604631971e12 10.99853 -9.15796 -4.06255 7.389451636363637 -5.325925181818182 -0.8366772727272725 120.96766216090002 83.86823136159998 16.5043125025 14.877506713996132 12.867072032207199 3.609078363636364 3.8320348181818176 3.2258727272727272 6.017872429752068 5.935532809917354 3.272427537190083 13.025446634868134 14.684490847757756 10.406254852561982 58.06359185692188 51.03102945179534 14.182854723662182 7.619946972054457 7.143600594363836 3.766013107207964
user_004 Jogging 1.446046321588e12 0.268841 -1.22565 -2.8363 7.4417064545454545 -5.629003000000001 -1.2163972727272727 7.2275483281e-2 1.5022179224999999 8.04459769 3.101465959152381 12.740650178610219 7.172865454545454 4.403353000000001 1.6199027272727273 6.5717763636363635 4.9743563966942155 3.4694130826446288 51.44999882901157 19.389517642609007 2.62408484582562 58.40254466676288 42.89118429085536 16.619887602393 7.642155760435852 6.549136148443957 4.076749636952581
user_004 Jogging 1.446046321782e12 17.43634 -13.52647 1.99206 6.964443727272727 -4.921818181818182 -1.3278746363636367 304.0259525956 182.9653906609 3.9683030435999997 22.15760921895907 12.77352648404185 10.471896272727275 8.604651818181818 3.3199346363636364 7.435724636363637 5.124153950413224 2.9639652231404954 109.66061154675938 74.04003291213967 11.02196598972695 83.41708559523506 48.905702732130756 12.350139861925124 9.133295440049833 6.993261237229077 3.514276577323578
user_004 Jogging 1.446046322106e12 2.8363 3.2195 -0.728685 6.306031000000001 -4.747634545454545 -0.878481909090909 8.04459769 10.36518025 0.530981829225 4.352098317963991 12.54258969286149 3.469731000000001 7.967134545454545 0.14979690909090893 8.468790429752065 5.474736917355371 2.3350062644628102 12.039033212361005 63.475232865375204 2.2439113973190032e-2 101.23215893633261 49.921877744916806 8.150795957230889 10.061419330111066 7.06554157477803 2.8549598871491852
user_004 Jogging 1.44604632366e12 5.32712 -4.5212 -1.45677 6.288613636363636 -3.427327727272727 -0.42908963636363634 28.378207494399998 20.441249440000004 2.1221788328999995 7.137340945148971 11.923127322944014 0.9614936363636364 1.0938722727272734 1.0276803636363636 7.177616363636364 4.30961020661157 2.8708571983471076 0.9244700127677686 1.1965565490415304 1.0561269298037685 77.96189106622585 30.35993183984033 14.367687461632316 8.829603109213112 5.50998474043625 3.7904732503517704
user_004 Jogging 1.446046324243e12 18.31771 -4.78944 -4.75232 7.950321818181819 -4.747635454545454 -0.6137233636363636 335.53849964410006 22.938735513599998 22.5845453824 19.52080378826907 13.319626558125197 10.367388181818182 4.180454545454548e-2 4.138596636363636 7.783457933884298 4.992408388429752 2.9075944876033057 107.48273771250331 1.7476200206611595e-3 17.127982118520404 88.54589721943135 43.57792982133113 14.303951790608876 9.409882954608488 6.60135818005137 3.782056555712629
user_004 Jogging 1.44604632502e12 10.76861 -6.89706 -2.8363 7.431255909090908 -5.155225454545455 -0.7461031818181819 115.96296133210001 47.5694366436 8.04459769 13.098740232010863 12.689672224531755 3.337354090909093 1.7418345454545445 2.090196818181818 7.685599090909091 5.095651487603306 2.1465720082644633 11.13793232810766 3.0339875837388397 4.368922738737396 83.11050275563464 42.10401614099903 7.893255732608974 9.11649618853837 6.488760755413859 2.8094938570157035
user_004 Jogging 1.446046325862e12 2.4531 1.53341 -2.6447 7.424289090909091 -5.782283636363636 -0.9133188181818181 6.01769961 2.3513462280999997 6.994438089999999 3.919628034405816 12.74499084081831 4.971189090909091 7.315693636363636 1.7313811818181817 7.254255867768593 4.8524280165289255 2.1795067768595042 24.712720977573554 53.5193733811314 2.9976807967541235 85.1353323510852 38.528028298417354 6.254722770446421 9.226880965477186 6.207094996728933 2.500944375720184
user_004 Jogging 1.446046326444e12 3.0279 -8.27659 3.21831 6.009921272727274 -4.468944545454545 -0.8819659999999998 9.16817841 68.5019420281 10.357519256099998 9.38230460463739 11.679075659240123 2.982021272727274 3.8076454545454554 4.100275999999999 7.1263116528925625 5.702759008264464 2.0436455454545452 8.892450870997992 14.498163907520668 16.812263276175994 77.13632860967306 50.43628684576454 6.854830669867261 8.782728995572677 7.101850945054011 2.6181731550581717
user_004 Jogging 1.446046327027e12 -11.95534 3.33447 -0.652044 7.8283936363636375 -5.684742636363636 -1.035247090909091 142.93015451559998 11.1186901809 0.42516137793599995 12.428757221638694 13.073047165181565 19.783733636363635 9.019212636363637 0.383203090909091 7.583939752066116 5.743929752066115 1.863444553719008 391.3961165945859 81.3461965799415 0.14684460888228107 84.7339938268665 47.89733585550444 4.888394068814038 9.205106942717531 6.920790117862587 2.210971295339231
user_004 Jogging 1.446046327481e12 2.14654 5.0972 -0.345482 7.354615454545454 -5.2457994545454545 -0.502246909090909 4.607633971599999 25.98144784 0.119357812324 5.541519613240037 13.876676857035937 5.208075454545454 10.342999454545454 0.15676490909090895 8.180594925619834 5.740446297520661 3.169501487603306 27.124049940238834 106.97763771672757 2.457523672228095e-2 92.56675458972168 48.67282173154718 15.583841577487318 9.621161810806514 6.9765909821020164 3.9476374678391273
user_004 Jogging 1.446046327804e12 -5.17264 -0.459245 -0.268841 8.615702454545454 -5.482688636363637 -1.390581 26.756204569600005 0.210905970025 7.2275483281e-2 5.199940963405835 12.93261929312298 13.788342454545454 5.023443636363637 1.12174 6.679451371900826 5.460486388429753 2.7520947190082645 190.11838764382054 25.234985967722317 1.2583006276 58.47676565362632 42.53433048268549 11.850820053741382 7.647010242809037 6.5218349015200845 3.4425020049001254
user_004 Jogging 1.446046328193e12 4.29247 -6.74378 -3.41111 7.511379727272726 -5.879826818181818 -0.561469090909091 18.425298700899997 45.4785686884 11.635671432099999 8.691348504196572 13.72575512172113 3.2189097272727265 0.8639531818181823 2.8496409090909087 7.710933487603305 5.303720909090909 2.9934193884297526 10.361379832330979 0.7464151003737611 8.12045331076446 84.34857147036209 41.62065769902936 12.905406871537634 9.184147835828977 6.451407420015369 3.592409619118849
user_004 Jogging 1.446046328517e12 13.02951 -4.59784 -1.45677 8.302171818181817 -5.517527272727272 -0.6555282727272727 169.7681308401 21.140132665599996 2.1221788328999995 13.893539589989299 13.923873828438145 4.727338181818183 0.9196872727272725 0.8012417272727272 6.949278479338843 5.963083636363636 2.9775846363636362 22.347726285276046 0.8458246796165284 0.6419883055229835 67.73211738082999 51.18097953516217 12.185358501479174 8.229952453133006 7.1540883091531775 3.490753285679063
user_004 Jogging 1.446046328711e12 10.30876 -6.39889 -4.17751 6.793744545454545 -4.280825454545455 -0.8436463636363635 106.27053273759999 40.945793232099994 17.4515898001 12.832299706981598 12.584073317230303 3.5150154545454546 2.118064545454545 3.3338636363636365 7.7533713471074375 5.513691611570248 2.685272330578513 12.355333645693388 4.486197418711568 11.11464674586777 84.63114349725714 45.01627098571577 10.222967980701204 9.19951865573722 6.709416590562533 3.197337639458993
user_004 Jogging 1.446046328775e12 13.02951 -13.18159 2.56686 7.246621818181817 -4.681447272727273 -1.0979545454545454 169.7681308401 173.7543149281 6.5887702596 18.711259071152853 13.097908141077136 5.782888181818183 8.500142727272728 3.6648145454545453 8.083053553719008 5.9361653719008265 2.462000578512397 33.44179572341242 72.25242638400745 13.430865652575205 87.2485802390777 50.235120648544374 8.038115823601757 9.340694847765754 7.08767385314423 2.835157107393126
user_004 Jogging 1.446046329099e12 2.72134 5.51872 -1.57173 6.4140263636363635 -4.204185454545454 -0.38380181818181813 7.405691395600001 30.4562704384 2.4703351929000004 6.350771372589318 12.235529986824947 3.6926863636363634 9.722905454545455 1.187928181818182 7.503815041322315 5.289469958677685 2.57411114876033 13.635932580185948 94.53489047802975 1.4111733651578515 82.5461956986643 43.85794114087185 9.103970994478788 9.085493695923425 6.622532834261515 3.017278739937493
user_004 Jogging 1.446046329423e12 -13.48815 6.70665 2.75846 6.807680909090909 -4.754605454545455 -0.411670909090909 181.93019042249998 44.9791542225 7.609101571599999 15.313995109591747 12.947341075284806 20.29583090909091 11.461255454545455 3.1701309090909087 7.943389752066116 5.935847603305786 2.3055521487603303 411.92075229040995 131.36037659434794 10.04972998077355 90.62691328474637 53.149538307322466 7.8468815671253935 9.519816872437534 7.29037298821689 2.801228581734342
user_004 Jogging 1.446046329747e12 6.63001 -6.55217 -2.52974 7.490478181818181 -5.7927363636363625 -0.5579845454545453 43.95703260010001 42.930931708900005 6.3995844675999995 9.658547964192133 13.755283506610226 0.860468181818181 0.7594336363636378 1.9717554545454545 7.370484462809916 5.440533140495867 2.5389578512396693 0.7404054919214862 0.576739448040498 3.887819572529752 86.65650687937087 45.48921107354072 10.158724405702777 9.308947678409782 6.744569005766101 3.1872753890592476
user_004 Jogging 1.446046331042e12 5.36544 -5.44089 -3.29615 6.971412818181818 -4.611773636363637 -1.4254168181818185 28.787946393600006 29.603283992099996 10.864604822499999 8.322009084842433 12.189372604813066 1.6059728181818178 0.8291163636363628 1.8707331818181814 7.043021834710743 5.3205052892561975 1.757984123966942 2.57914869273885 0.6874339444495853 3.499642637555577 80.72587526909831 45.50673615751014 4.841566405525911 8.984757941597442 6.745868080351864 2.2003559724567094
user_004 Jogging 1.446046331301e12 8.62267 -8.08499 -2.14654 7.929420090909091 -5.778801818181818 -0.7321687272727274 74.35043792889999 65.36706330009999 4.607633971599999 12.013539661590167 13.457641481202769 0.6932499090909081 2.3061881818181815 1.4143712727272724 6.823233702479339 5.110853140495868 2.27198279338843 0.4805954364545524 5.31850392995785 2.000446097116164 78.5674392359401 42.57444091505011 7.554090073221997 8.863827572552395 6.524909264890211 2.74847049706232
user_004 Jogging 1.446046331366e12 2.41478 1.91661 -2.56806 7.877165545454544 -6.092331818181818 -0.7879078181818183 5.8311624484 3.6733938920999996 6.5949321636 4.012416790925389 13.236432239904314 5.462385545454545 8.008941818181817 1.7801521818181816 6.9201424710743815 4.9287523140495875 2.3429231487603306 29.837655847190746 64.14314904702148 3.168941790432032 79.52284094580611 39.29280324603133 7.751301455787282 8.91755801471491 6.2683971831746055 2.7841159199622565
user_004 Jogging 1.446046331431e12 3.37279 5.97857 -0.996927 7.305844636363634 -4.664029090909091 -0.7948751818181818 11.375712384100002 35.7432992449 0.993863443329 6.936344503578884 12.617753455719923 3.933054636363634 10.64259909090909 0.20205181818181817 6.99963297520661 5.3638941322314055 2.3321552892561983 15.468918772621478 113.264915409819 4.0824937230578506e-2 80.07861579473527 46.472050661991666 7.7456747098245025 8.948665587378672 6.817041195562168 2.783105227946745
user_004 Jogging 1.44604633195e12 1.26517 -6.62882 4.09967 5.915862727272727 -5.0019445454545455 -0.9063518181818183 1.6006551288999997 43.9412545924 16.8072941089 7.896151203605463 12.055525367001298 4.650692727272727 1.6268754545454547 5.006021818181818 7.00184850413223 6.076778429752067 1.7598838595041322 21.628942843507435 2.64672374460248 25.060254444112395 77.09111527379356 54.937435054831184 5.864779279585238 8.780154626986564 7.411979159093149 2.421730637289217
user_004 Jogging 1.446046332532e12 -12.91335 6.32345 2.56686 7.016699090909091 -5.4408854545454535 -0.6346270909090911 166.7546082225 39.986019902500004 6.5887702596 14.605800162421778 13.1229795705556 19.93004909090909 11.764335454545453 3.201487090909091 7.725817520661158 5.990320991735536 1.863444090909091 397.20685676604626 138.39958868707515 10.249519593257554 85.67383220578002 55.77066896003064 5.5127307761822175 9.256016000730552 7.467976229208998 2.347920521691954
user_004 Jogging 1.44604633454e12 1.07357 1.76333 -1.87829 7.535765454545455 -6.231677818181819 -0.5092127272727273 1.1525525448999998 3.1093326889000004 3.5279733241 2.7910318088298456 13.807935746420464 6.462195454545455 7.9950078181818185 1.3690772727272726 7.731201818181817 5.40981482644628 3.0716415289256203 41.75997009274794 63.920150012788405 1.874372578698347 85.4124436525303 46.33350515713057 12.281585867258803 9.241885286700452 6.806871906913671 3.5045093618449363
user_004 Jumping 1.446046441012e12 0.11556 -7.6042e-2 0.229323 3.066224636363637 -2.347390636363636 -1.0352460909090908 1.3354113599999998e-2 5.782385764e-3 5.2589038329e-2 0.2678162386656194 6.663820669302523 2.950664636363637 2.2713486363636357 1.2645690909090908 3.4318280515741835 4.729928820297126 1.460011539288994 8.706421796286955 5.159024627910948 1.5991349856826442 30.129378939789817 43.53396871999754 4.327364124772764 5.489023496013641 6.598027638620312 2.080231747852331
user_004 Jumping 1.446046442049e12 -0.689167 2.8363 -3.06622 3.2856952727272737 -2.413580636363636 -0.944672090909091 0.47495115388899994 8.04459769 9.4017050884 4.233350201942782 7.329990664988696 3.9748622727272735 5.2498806363636366 2.121547909090909 4.880614909090909 5.935214314049587 1.7291644628099172 15.799530087150627 27.56124669606586 4.500965530568007 34.00485376745251 45.978269371149565 5.211924030871701 5.831368087117508 6.780727790668902 2.2829638698130337
user_004 Jumping 1.446046442438e12 19.39068 -8.54483 -1.99325 7.2849425454545464 -5.810152818181818 -1.181561090909091 375.9984708624 73.01411972889998 3.9730455625 21.28345921493496 11.312772133446702 12.105737454545453 2.7346771818181814 0.811688909090909 5.988737355371901 5.692940950413223 1.6680408677685947 146.54887931838462 7.478459288757031 0.6588388851411898 55.298300085495065 49.287809343806956 4.708620974921443 7.436282679235309 7.020527711205687 2.169935707554821
user_004 Jumping 1.446046444381e12 0.575403 1.68669 0.804128 3.881401636363636 -2.943098090909091 -1.0108614545454546 0.331088612409 2.8449231561 0.646621840384 1.955155648252333 6.825409119985633 3.305998636363636 4.629788090909091 1.8149894545454546 5.655888628099174 5.312588950413223 1.0774021487603307 10.929626983638219 21.43493776672365 3.2941867201112065 39.46488549288111 40.36311851017048 1.4810578740002074 6.282108363669089 6.353197502846144 1.2169872119296108
user_004 Jumping 1.446046444705e12 -1.72382 1.26517 -1.45677 3.4250405454545447 -2.538992090909091 -0.8645478181818181 2.9715553923999996 1.6006551288999997 2.1221788328999995 2.5873518033309653 7.430472593829023 5.148860545454545 3.8041620909090907 0.5922221818181818 5.885177429752065 5.714477388429751 1.623387438016529 26.51076491653847 14.471649213909826 0.3507271126374875 41.50646022554733 48.4089620683375 4.0390436543496975 6.442550754596143 6.957654925931402 2.0097372102714566
user_004 Jumping 1.446046445352e12 1.61005 -0.689167 -0.613724 3.421557363636364 -2.8525229090909097 -0.6764302727272727 2.5922610025 0.47495115388899994 0.37665714817600005 1.8557665005503792 6.618484100427451 1.811507363636364 2.16335590909091 6.27062727272727e-2 4.69249785123967 4.731132884297521 1.220549396694215 3.2815589285087703 4.680108789398557 3.9320766393471035e-3 32.01619088385683 36.76868457832758 2.1039822892654296 5.658285153989398 6.063718708707354 1.4505110441721667
user_004 Jumping 1.446046445417e12 0.230521 0.958607 -0.805325 3.5992247272727274 -2.8803922727272733 -0.617208 5.3139931441e-2 0.918927380449 0.6485483556249999 1.2730340402027749 6.499000667415796 3.3687037272727274 3.838999272727273 0.18811699999999998 4.530665413223141 4.734299900826446 1.183812561983471 11.348164802141167 14.737915416000531 3.538800568899999e-2 30.637772691638897 36.79289059669946 2.075315097724658 5.535139807777116 6.06571435172309 1.440595396953863
user_004 Jumping 1.446046445934e12 0.537083 1.38013 0.574206 3.4215574545454546 -2.901293363636363 -0.6938475454545454 0.28845814888899995 1.9047588169000003 0.329712530436 1.5883732232145569 6.391787495405162 2.8844744545454546 4.281423363636363 1.2680535454545454 4.553151033057851 4.739684735537191 1.0140632314049587 8.320192878925297 18.33058601869131 1.607959794139843 30.362919934925173 34.44872365056209 1.8205224073468378 5.510255886519715 5.869303506427495 1.3492673594758149
user_004 Jumping 1.446046446453e12 3.8919e-2 1.26517 -1.15021 3.5400021818181817 -2.8002671818181812 -0.885449909090909 1.514688561e-3 1.6006551288999997 1.3229830441 1.710307826550823 6.409141424665947 3.501083181818182 4.065437181818181 0.2647600909090909 4.330829314049587 4.661143809917356 1.3735138842975205 12.257583446010123 16.527779479309753 7.009790573819008e-2 29.248410111056636 32.12759086779462 2.7849106541989044 5.408179925913767 5.668120576328156 1.668805157649899
user_004 Jumping 1.446046446647e12 14.524 -16.51545 -2.95126 6.344352909090909 -5.663839181818181 -1.2756198181818181 210.94657599999996 272.76008870250007 8.7099355876 22.190461921512586 10.221041190898104 8.17964709090909 10.85161081818182 1.6756401818181819 5.734112421487603 6.297515892561984 1.6347882066115702 66.90662653181752 117.75745734928071 2.8077700189236694 47.85472337486385 53.796944082781586 3.402840660552115 6.917710847879077 7.334640010442339 1.8446790128778814
user_004 Jumping 1.446046447294e12 0.690364 6.13185 -2.41478 4.372599 -3.9324581818181814 -0.8088090909090909 0.476602452496 37.5995844225 5.8311624484 6.626262092869252 9.25374689473398 3.6822350000000004 10.06430818181818 1.605970909090909 5.767999487603306 6.21485658677686 1.7959872231404963 13.558854595225002 101.29029917861237 2.5791425608462806 46.44946369914939 57.41211919025554 6.140247961835453 6.815384339796942 7.577078539269309 2.477952372794008
user_004 Jumping 1.446046447553e12 -0.305964 0.15388 0.919089 3.3518848181818184 -2.8490389090909094 -0.7321676363636364 9.361396929600001e-2 2.3679054399999996e-2 0.8447245899210001 0.9808249658410007 6.6372655762031405 3.6578488181818183 3.0029189090909094 1.6512566363636365 4.801757578512397 4.826141876033057 1.389348479338843 13.379857976674124 9.017521974575738 2.726648479134951 36.44454048917954 40.37524681559476 3.9165839136820506 6.036931380194704 6.3541519351991225 1.979036107220394
user_004 Jumping 1.446046447877e12 -2.0687 1.26517 -2.68302 2.752694363636364 -2.389195181818182 -0.8227430909090908 4.279519690000001 1.6006551288999997 7.1985963204 3.6164583696345796 7.513186647834316 4.821394363636364 3.6543651818181817 1.860276909090909 5.199528041322314 5.300553785123967 2.2431630661157027 23.2458436097045 13.354384882085032 3.4606301784968263 35.31507716132555 44.82950662438718 7.178032604310255 5.94264900202978 6.695484047056432 2.679185063468042
user_004 Jumping 1.446046448266e12 7.05154 -11.99366 0.765807 6.215457636363637 -6.033109090909092 -1.5786987272727273 49.7242163716 143.8478801956 0.586460361249 13.934078976683352 11.008782920283485 0.836082363636363 5.960550909090908 2.344505727272727 5.663172289256199 5.973218016528926 2.258681280991735 0.6990337187837675 35.52816713986445 5.49670710521462 48.64535340019356 54.29968853739611 8.110638392927495 6.974622097303449 7.368832237023455 2.8479182560121865
user_004 Jumping 1.446046448589e12 0.613724 1.38013 -1.30349 3.432009090909091 -2.922197090909091 -1.035247090909091 0.37665714817600005 1.9047588169000003 1.6990861801000001 1.995119581673239 6.530676980772938 2.818285090909091 4.302327090909091 0.2682429090909091 4.197816942148761 4.6481589338842975 1.5796834132231403 7.942730853640462 18.51001839717028 7.195425827755372e-2 30.439595937202203 32.74221239276296 5.038458929277009 5.517209071369527 5.7220811242731395 2.2446511820942265
user_004 Jumping 1.446046451632e12 0.383802 5.02056 -2.0699 4.059068 -2.8838754545454544 -1.0317637272727274 0.147303975204 25.206022713599996 4.28448601 5.444062150527306 8.16787770960744 3.6752659999999997 7.904435454545454 1.0381362727272727 5.191295008264462 5.4522509917355375 1.6376389090909091 13.507580170755999 62.480099855075196 1.0777269207520743 41.150174406921245 43.123580354647196 3.595734975028297 6.414840170021483 6.5668546774424055 1.8962423302490368
user_004 Jumping 1.446046451892e12 -0.382604 0.690364 7.6042e-2 3.557419909090909 -2.660921272727273 -1.2129147272727272 0.146385820816 0.476602452496 5.782385764e-3 0.7929506031752546 6.9635497729535 3.9400239090909093 3.3512852727272726 1.2889567272727271 5.185593942148761 4.676977388429751 1.325692917355372 15.523788404208009 11.23111297919871 1.6614094447816194 39.5295646746675 36.15230679208021 2.620653828008208 6.287254144272164 6.0126788365985595 1.6188433611712432
user_004 Jumping 1.44604645228e12 -1.95374 -1.72382 0.919089 3.003517363636363 -2.389195818181818 -1.2338168181818183 3.8170999876000002 2.9715553923999996 0.8447245899210001 2.7628572112798375 7.240861773271672 4.957257363636363 0.6653758181818179 2.1529058181818184 4.876497239669423 5.02154452892562 1.697495950413223 24.574400569326944 0.4427249794211236 4.635003461961125 32.368275452791906 40.1732580945433 5.756142783581481 5.689312388399138 6.338237775166162 2.39919627866948
user_004 Jumping 1.446046452538e12 18.54763 -15.40417 -3.98591 4.9648212727272725 -3.9847141818181813 -1.3940644545454548 344.01457861690005 237.28845338890002 15.8874785281 24.437481673321006 8.936126658691224 13.58280872727273 11.41945581818182 2.5918455454545453 5.416781504132231 5.744247553719009 1.6895778347107437 184.49269292167622 130.4039711834066 6.717663331492569 45.55107155931277 48.760047922413534 5.977856426539219 6.749153395746222 6.982839531480981 2.444965526656607
user_004 Jumping 1.446046453251e12 -1.83878 -3.33327 4.02303 5.341056181818182 -4.782472272727273 -0.7879082727272727 3.3811118884000004 11.1106888929 16.1847703809 5.538643440608901 10.00383736993665 7.179836181818182 1.4492022727272729 4.810938272727273 5.844640479338843 5.239432685950413 1.737398876033058 51.55004759774549 2.100187227277893 23.145127063992078 47.490441190720986 50.018904538781086 5.802457122441708 6.891330872242385 7.072404438292615 2.4088289940221386
user_004 Jumping 1.446046453445e12 3.0279 -1.45557 -7.7239e-2 3.675864363636364 -2.6922731818181824 -1.1362745454545455 9.16817841 2.1186840249000003 5.965863121e-3 3.3604803671530354 7.688581707506595 0.6479643636363641 1.2367031818181824 1.0590355454545455 5.11655426446281 4.447690247933884 1.4346366611570247 0.4198578165426783 1.5294347599192164 1.1215562865362068 38.29682912226736 35.61574287410279 4.090531801082638 6.1884431905179 5.967892666101058 2.0225063166978337
user_004 Jumping 1.446046454158e12 0.652044 1.72501 -1.03525 2.9965505454545447 -2.4797716363636364 -1.2582024545454547 0.42516137793599995 2.9756595001 1.0717425625 2.114843597180652 6.536228248549308 2.3445065454545446 4.204781636363636 0.22295245454545465 4.096157082644628 4.746651454545454 1.610085991735537 5.496710941679202 17.680188609500856 4.970779698784302e-2 26.08166873535217 35.08718337156006 6.381092379007582 5.107021513108416 5.923443539999353 2.5260824173030425
user_004 Jumping 1.446046454675e12 0.345482 2.4531 -1.99325 3.397172363636363 -2.6365361818181823 -1.1815614545454545 0.119357812324 6.01769961 3.9730455625 3.1796388135799325 7.349200198128122 3.051690363636363 5.089636181818182 0.8116885454545455 4.695980223140495 5.221379603305784 1.5765160165289254 9.312814075511037 25.904396463272764 0.6588382948221158 35.95807892190684 44.31499999041549 5.402094381806359 5.9965055592325465 6.656951253420404 2.3242406032522447
user_004 Jumping 1.44604645487e12 12.22478 -14.1396 -1.03525 6.717105181818181 -6.022658545454546 -1.592634181818182 149.4452460484 199.92828816 1.0717425625 18.720183673535363 11.750544288016998 5.50767481818182 8.116941454545454 0.557384181818182 6.046375016528926 6.576525785123966 1.9524353471074383 30.334481902834142 65.88473857651847 0.3106771261411241 55.06290521812116 67.83194182478591 6.36341218656381 7.420438344068439 8.236014923783584 2.522580461861189
user_004 Jumping 1.44604645597e12 8.77595 -13.18159 0.804128 6.455829454545454 -6.026142454545454 -1.568247545454546 77.0172984025 173.7543149281 0.646621840384 15.85617340883304 11.218761559924888 2.3201205454545457 7.155447545454546 2.372375545454546 5.748047107438017 5.903544363636365 2.0901981487603303 5.382959345440299 51.200429575751485 5.628165728670754 50.331598154741954 56.07913702398294 6.685448936200232 7.094476594840662 7.488600471649088 2.585623510142231
user_004 Jumping 1.446046456165e12 -2.03038 0.383802 0.344284 3.4389759090909084 -1.9363195454545457 -1.3766462727272726 4.1224429444 0.147303975204 0.11853147265599999 2.094821804416786 7.445358468937255 5.4693559090909085 2.320121545454546 1.7209302727272726 4.207634471074379 5.526991512396695 1.8906791074380165 29.91385406030764 5.38296398568239 2.961601003589165 28.717641389713194 45.835480733710945 5.353617666866859 5.35888434188621 6.77019059803422 2.3137885959756264
user_004 Jumping 1.446046456553e12 -3.7722e-2 -8.19995 4.44456 5.818319 -5.827572363636364 -1.2756197272727272 1.422949284e-3 67.23918000249999 19.7541135936 9.327095825892645 10.682069515574172 5.856040999999999 2.3723776363636357 5.720179727272727 6.01913994214876 6.165136165289257 2.8100497024793394 34.29321619368099 5.628175649518311 32.72045611230189 52.990159518859336 53.34973957557859 10.45758717127323 7.279434010887065 7.304090605652328 3.233819285500232
user_004 Standing 1.446046405273e12 1.03525 -9.34956 0.152682 1.0666006363636364 -9.363494545454545 0.1875190909090909 1.0717425625 87.41427219360001 2.3311793124000002e-2 9.407939548552807 9.43353814467717 3.135063636363644e-2 1.3934545454544534e-2 3.48370909090909e-2 0.16144091391512527 5.332828964974403e-2 0.1500458602879444 9.828624004049637e-4 1.941715570247677e-4 1.2136229030082638e-3 5.7123950662914674e-2 6.371192410501708e-3 3.864845095038317e-2 0.23900617285525216 7.981974950162214e-2 0.1965920927972007
user_004 Standing 1.446046405402e12 0.958607 -9.38788 0.152682 1.0073788181818184 -9.370461818181816 0.239774 0.918927380449 88.13229089439999 2.3311793124000002e-2 9.437930391138355 9.428698068400793 4.8771818181818416e-2 1.7418181818182887e-2 8.709199999999997e-2 7.313571143578647e-2 2.904839984258151e-2 0.10803079004001047 2.3786902487603536e-3 3.0339305785127694e-4 7.5850164639999955e-3 7.137901634508789e-3 1.51052916609067e-3 1.8586924123821767e-2 8.448610320347831e-2 3.886552670543228e-2 0.13633387005370956
user_004 Standing 1.446046406114e12 1.03525 -9.38788 -0.11556 0.9760256363636363 -9.387879999999997 2.7270636363636358e-2 1.0717425625 88.13229089439999 1.3354113599999998e-2 9.445495623338141 9.439062086037746 5.922436363636374e-2 1.7763568394002505e-15 0.14283063636363635 5.573941322314055e-2 3.0085950413224018e-2 9.37422396694215e-2 3.507525248132244e-3 3.1554436208840472e-30 2.040059068404132e-2 4.640469144164543e-3 1.4684224000000342e-3 1.0355239224131481e-2 6.812098901340571e-2 3.8320000000000444e-2 0.10176069587090823
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user_005 Jogging 1.446046538656e12 -0.574206 -15.82569 -16.24841 -5.19702809090909 -18.058719090909094 -1.2756189999999998 0.329712530436 250.4524639761 264.0108275281 22.68905031143075 21.186891005724313 4.622822090909089 2.2330290909090937 14.972791 6.20567385123967 4.47017479338843 6.922676074380166 21.370484084197084 4.986418920846294 224.18447032968103 46.22914933865778 25.025719547759216 86.75529880896889 6.799202110443384 5.002571293620833 9.314252455724446
user_005 Jogging 1.446046538696e12 8.31611 -6.74378 -7.08986 -2.2846848181818173 -15.250886363636367 -7.6855626363636365 69.1576855321 45.4785686884 50.2661148196 12.84143173637971 19.358054965294073 10.600794818181818 8.507106363636368 0.5957026363636366 6.402976165289258 4.645308099173556 7.665329388429751 112.37685077719048 72.37085868222238 0.3548616309705871 49.725863424499494 26.103591191193857 94.9418704171257 7.051656785784423 5.109167367702281 9.743811903825202
user_005 Jogging 1.446046538753e12 -15.44249 -0.344284 -2.18486 -2.319522727272727 -4.169348636363636 -7.828393636363637 238.4704974001 0.11853147265599999 4.7736132196000005 15.600084682217465 14.044445408721396 13.122967272727273 3.825064636363636 5.643533636363637 9.416029735537188 7.42495634710744 1.6822933057851244 172.21227004107106 14.631119472359673 31.849471904767775 103.95241120687697 62.264699145702394 5.839061575357855 10.195705527665899 7.890798384555418 2.416415025478416
user_005 Jogging 1.446046538776e12 -7.31858 1.03525 -6.20849 -5.831056363636363 -0.9539253636363635 -6.699686636363636 53.5616132164 1.0717425625 38.545348080100005 9.652911677778887 13.13116332092457 1.4875236363636368 1.9891753636363636 0.491196636363636 8.796887380165288 6.473283157024794 2.240312190082645 2.2127265687404973 3.956818627297859 0.24127413557495003 98.15646520194038 54.52746920713473 10.183716786829123 9.907394470895987 7.384271745211895 3.1911936304193644
user_005 Jogging 1.446046538842e12 -1.34061 -9.96268 1.26397 -3.106829272727273 -2.922194636363636 -2.5018703636363635 1.7972351721000002 99.25499278240001 1.5976201609 10.131626133814848 7.283615235429099 1.766219272727273 7.040485363636364 3.7658403636363635 5.634669446280991 2.638084099173554 3.2736945206611576 3.119530519353257 49.56843415557786 14.181553644392858 39.12376106844633 10.021174904445111 13.79509503835697 6.254898965486679 3.1656239360424845 3.7141748798834135
user_005 Jogging 1.446046538866e12 2.56806 -19.46612 0.382604 -0.3930543636363636 -7.370835181818182 -0.9760242727272725 6.5949321636 378.9298278544 0.146385820816 19.638511803057177 8.868827912159022 2.9611143636363635 12.095284818181817 1.3586282727272725 4.628840950413223 4.8574955537190085 3.348752347107438 8.768198274533585 146.29591483293956 1.8458707834538919 30.46137151071938 38.590619390286015 13.792196038869717 5.51918214146982 6.212134849654023 3.7137845978017783
user_005 Jogging 1.446046538922e12 11.22845 -19.58108 -6.70665 9.591128545454545 -17.738221818181817 -2.181371454545454 126.07808940250001 383.4186939664 44.9791542225 23.54731274671061 21.66341615767337 1.6373214545454555 1.8428581818181833 4.525278545454546 6.907156999999999 7.350216272727274 3.8332976611570246 2.680821545514846 3.3961262782942203 20.47814591395121 76.23218786568253 63.583759756504904 17.994963219286294 8.731104618871688 7.973942547855791 4.242047055289025
user_005 Jogging 1.446046539109e12 -2.2603 -0.574206 -1.34181 2.0246095454545454 6.494150545454545 5.46527 5.1089560899999995 0.329712530436 1.8004540760999999 2.690561780843547 9.417106115997395 4.284909545454545 7.068356545454545 6.80708 3.0412402148760322 7.885117867768597 3.5615710909090903 18.360449812727477 49.961664253670115 46.3363381264 14.181878532462372 92.28869650125806 17.74296814917574 3.7658834995870984 9.606700604331232 4.212240276761968
user_005 Jogging 1.446046539173e12 4.06255 -8.54483 1.91542 -0.19448763636363625 -6.102783090909091 -6.051724545454545 16.5043125025 73.01411972889998 3.6688337763999996 9.653355168427193 10.091842877452285 4.257037636363636 2.442046909090908 7.967144545454545 2.8762417603305788 7.647278181818183 8.382647024793387 18.12236943741649 5.963593106200457 63.475392208166106 10.35465508928085 63.68957512102852 83.8630590189311 3.2178649892872837 7.980574861564079 9.157677599639065
user_005 Jogging 1.446046539182e12 4.82896 -4.63616 12.56846 0.18174836363636357 -6.64623490909091 -5.041461818181818 23.318854681600005 21.493979545600002 157.9661867716 14.240049894533376 11.19579267288441 4.647211636363637 2.0100749090909096 17.609921818181817 3.0523252975206607 7.180150446280991 9.50597 21.596575993153593 4.0404011401568285 310.109346442476 11.650190482521412 59.41136010555187 109.54591898594536 3.41323753678548 7.7078764978139 10.4664186322708
user_005 Jogging 1.446046539432e12 -18.54643 -1.80046 -9.04419 1.334843636363636 -7.889902181818181 -10.256508181818182 343.9700657449 3.2416562115999996 81.7973727561 20.712534724475418 17.463259594868898 19.881273636363638 6.089442181818181 1.2123181818181816 11.065702727272729 6.9714458099173555 4.298841314049587 395.2650414039678 37.081306085706565 1.4697153739669417 142.99720294716028 63.301853957224964 38.408486209862765 11.95814379187507 7.956246222762652 6.197458044219643
user_005 Jogging 1.446046539505e12 0.920286 -2.29862 0.191003 -9.147504363636365 -2.525057909090909 -5.947214272727273 0.8469263217960001 5.2836539044 3.6482146009e-2 2.483357077064231 13.013596496583101 10.067790363636366 0.226437909090909 6.138217272727274 10.895003123966942 3.147332603305786 3.7512741322314045 101.36040280612927 5.127412667346277e-2 37.67771128720745 152.4638426241614 15.151679892008083 18.234761740799325 12.34762497908652 3.8925158820495622 4.270217996870807
user_005 Jogging 1.44604653965e12 -2.14534 -19.58108 -9.00587 9.608546363636364 -19.581079999999996 -4.916048636363636 4.6024837156 383.4186939664 81.1056944569 21.659336835159564 23.481648866437364 11.753886363636365 3.552713678800501e-15 4.089821363636363 8.339577099173555 4.43375396694215 3.665448603305785 138.1538446492769 1.2621774483536189e-29 16.7266387864564 83.59105699229161 33.67984891858641 16.49654774616765 9.142814500595078 5.803434234880792 4.061594237016747
user_005 Jogging 1.446046539716e12 4.56072 14.40904 7.93171 -1.375448818181818 -7.924737636363636 -1.4530909090908766e-2 20.8001669184 207.62043372159997 62.9120235241 17.06846871175326 17.391907634086433 5.936168818181818 22.333777636363635 7.946240909090909 8.200547190082643 8.98468811570248 6.25096247107438 35.23810023795412 498.7976235105364 63.14274458530991 88.97410851906962 181.6387913741941 46.31359502348609 9.432608786495368 13.477343631969696 6.805409247318348
user_005 Jogging 1.446046539747e12 0.690364 8.92923 11.18893 -0.5393693636363636 3.6723814545454547 7.140916363636364 0.476602452496 79.73114839290001 125.19215454489998 14.331779561181367 15.617158981160749 1.2297333636363637 5.256848545454545 4.048013636363635 6.121115801652894 13.546704859504132 7.083557809917355 1.512244145640405 27.63445662984757 16.386414400185938 58.020580521352855 251.58207109683693 54.824987122639506 7.617124163445995 15.861338880965784 7.404389719797271
user_005 Jogging 1.446046539885e12 4.29247 -6.05401 17.28186 0.8366770909090909 -8.346261727272728 -5.407247272727274 18.425298700899997 36.6510370801 298.66268505960005 18.80795100059015 13.44750584742789 3.455792909090909 2.2922517272727276 22.689107272727277 1.5008245041322312 7.227337421487603 11.299107636363637 11.942504630523008 5.254417981184804 514.7955888333258 2.962468411960157 61.79855321610177 154.19796079881098 1.7211822715680514 7.861205582867158 12.41764715229141
user_005 Jogging 1.446046540023e12 -7.66346 -19.58108 -3.60271 -2.960515727272728 -14.83632909090909 5.266703363636363 58.728619171599995 383.4186939664 12.9795193441 21.333701799783835 17.67996709949153 4.702944272727272 4.744750909090911 8.869413363636363 6.033707289256199 4.108823966942149 4.649743338842975 22.117684832378252 22.512661189319026 78.6664934150513 37.483704938843324 25.68529101098272 33.9780325674715 6.1223937262188 5.06806580570761 5.829067898684275
user_005 Jogging 1.446046540039e12 -0.650847 -19.58108 -15.36704 -3.378555909090909 -16.710539999999995 0.7692924545454531 0.42360181740899994 383.4186939664 236.14591836159997 24.899562529197354 19.24158714860748 2.727708909090909 2.8705400000000054 16.136332454545453 5.15487405785124 4.64119132231405 6.272813537190083 7.440395892733917 8.23999989160003 260.38122508361687 30.22391534719549 27.7202941407852 67.74329423298182 5.497628156504902 5.265006566072373 8.230631460160382
user_005 Jogging 1.446046540137e12 -19.58108 -2.4519 -5.97857 -0.6334290909090909 -4.963624090909092 -8.80382090909091 383.4186939664 6.011813610000001 35.7432992449 20.619743131797254 16.05909241623178 18.94765090909091 2.511724090909092 2.825250909090909 10.737920123966942 7.628275264462809 3.242024851239669 359.0134749727736 6.308757908853104 7.982042699319007 145.38484253940564 74.57561519999079 14.833590141372897 12.057563706628533 8.63571741084612 3.851440008798384
user_005 Jogging 1.446046540145e12 -17.12858 -2.8351 -2.8363 -2.3613263636363637 -3.768726818181818 -7.978191818181819 293.3882528164 8.03779201 8.04459769 17.591777696310285 15.838120119261502 14.767253636363636 0.9336268181818177 5.1418918181818185 11.628155049586777 7.521232082644629 2.953197190082645 218.071779960695 0.8716590356283049 26.439051469885126 162.9597919738336 74.24969775898148 10.945713369493298 12.765570569850516 8.616826431986517 3.3084306505491843
user_005 Jogging 1.446046540153e12 -12.98999 -3.79311 -1.91661 -3.9289754545454545 -2.9779350000000004 -7.319779090909091 168.73984020010002 14.387683472099999 3.6733938920999996 13.667513218003487 15.62031062188086 9.061014545454546 0.8151749999999995 5.403169090909092 11.8254576446281 7.077222702479339 3.0627749834710745 82.10198459293885 0.6645102806249993 29.194236224955382 166.10710388677384 71.3572194396066 11.99776784122342 12.888254493404988 8.447320251985632 3.463779415786089
user_005 Jogging 1.44604654025e12 -1.83878 -15.55745 2.79678 -2.1383713636363635 -7.443994545454546 -1.1293063636363634 3.3811118884000004 242.0342505025 7.8219783684 15.913432714511975 9.685510859791448 0.2995913636363634 8.113455454545452 3.9260863636363634 4.633590479338844 3.3725050578512397 5.092800735537191 8.975498516549572e-2 65.82815941289334 15.414154134731403 36.68492211564025 18.14740033356985 28.118351554473097 6.056807914705588 4.259976564908526 5.302674000395753
user_005 Jogging 1.446046540339e12 -2.10702 -19.58108 -9.65732 9.967363636363636 -19.52882545454545 -3.710701727272727 4.439533280399999 383.4186939664 93.2638295824 21.934494679139522 23.708771637632957 12.074383636363637 5.225454545454866e-2 5.946618272727273 9.42869852892562 4.468590330578514 4.145560669421488 145.79074019808596 2.730537520661492e-3 35.36226888153389 110.2410839227691 32.07802959815651 22.283775548103858 10.499575416309419 5.6637469574616865 4.720569409308993
user_005 Jogging 1.446046540363e12 -8.04667 -18.39315 -0.345482 6.685750909090908 -19.47308636363636 -3.8570151818181815 64.7488980889 338.30796692249993 0.119357812324 20.07924856222772 23.737894362214355 14.732420909090909 1.0799363636363601 3.5115331818181814 11.771304966942148 2.058528099173556 3.738288214876033 217.044225842619 1.1662625495041248 12.330865287010122 156.6251399409877 8.933381865150865 18.66196161047686 12.514996601716986 2.98887635494526 4.319949260173881
user_005 Jogging 1.446046540522e12 -0.305964 -7.66346 -11.42005 -2.5564122727272727 -6.144585272727273 -0.2897438181818185 9.361396929600001e-2 58.728619171599995 130.4175420025 13.756444858443478 15.856074884135257 2.2504482727272728 1.5188747272727268 11.130306181818181 8.48620773553719 8.865609454545456 7.248238735537189 5.064517428221166 2.3069804371478 123.88371570102001 99.27292641162785 168.106297538483 65.30499509597418 9.96357999976052 12.965581264967762 8.081150604708105
user_005 Jogging 1.446046540563e12 4.33079 -10.57581 1.14901 1.3104566363636363 -4.935754363636364 -4.727931818181819 18.7557420241 111.84775715610002 1.3202239801000002 11.485805290022116 16.556757493226794 3.020333363636364 5.640055636363637 5.87694181818182 3.7015521404958673 12.720126892561984 11.229750066115702 9.122413627494954 31.81022758127723 34.53844513429423 17.429640415905563 216.0190225727229 139.08506675730447 4.174882084072023 14.697585603517432 11.793433204851947
user_005 Jogging 1.446046540772e12 9.84892 -3.83143 -8.16283 1.1084052727272726 -15.58183272727273 -8.211596636363636 97.00122516639999 14.6798558449 66.6317936089 13.353384388244052 19.918923756128933 8.740514727272727 11.750402727272728 4.8766636363636096e-2 4.9981088264462805 5.275534958677687 8.059300198347106 76.39659769767142 138.07196425309837 2.3781848222231144e-3 32.22934544619266 35.61825024324111 88.64155595144413 5.677089522474756 5.968102733971753 9.414964468942202
user_005 Jogging 1.446046540854e12 -3.29495 -2.10702 -10.80693 -7.353418181818182 -1.340610909090909 -7.194366363636362 10.856695502500001 4.439533280399999 116.7897360249 11.492865822230764 13.606203557970458 4.058468181818182 0.7664090909090908 3.612563636363637 8.992923157024794 6.162287355371903 2.2906684793388425 16.471163982830582 0.587382894628099 13.050616026776865 111.40156660610614 74.20178893073263 8.095774139881183 10.554694055542592 8.614046025575474 2.845307389348501
user_005 Jogging 1.446046541081e12 -3.44823 5.36544 7.05034 3.9057872727272724 -14.17094909090909 -1.7946854545454547 11.8902901329 28.787946393600006 49.70729411560001 9.507130515676115 18.02446220678441 7.354017272727273 19.53638909090909 8.845025454545455 7.398668760330579 5.379727933884299 4.1227583057851245 54.08157004757107 381.6704987113917 78.23447529155703 64.79961115705889 68.58351805693644 24.705710676729385 8.049820566761653 8.281516651974833 4.970483947940018
user_005 Jogging 1.446046541105e12 0.690364 15.78857 11.91702 0.9760253636363636 -5.280636363636363 1.9885736363636362 0.476602452496 249.2789426449 142.0153656804 19.793203651197953 16.32681821965846 0.28566136363636363 21.06920636363636 9.928446363636365 5.796183347107438 10.402856280991735 6.1030641818181826 8.160241467458677e-2 443.91145679349495 98.57404719560415 47.5425530104997 191.3152041219281 46.42550130267332 6.895110804802175 13.831673945041073 6.813626149318241
user_005 Jogging 1.446046541161e12 3.33447 3.52607 4.7128 1.1502080909090908 9.664284545454546 10.102029090909092 11.1186901809 12.4331696449 22.21048384 6.764787037727056 14.376779236094603 2.1842619090909094 6.138214545454546 5.389229090909092 3.1340315041322313 12.022759669421486 6.602495041322314 4.771000087505464 37.677677806029756 29.04379019430084 12.984159483889442 206.43890998226743 57.00039092718214 3.60335392154163 14.367982112400734 7.549860325011459
user_005 Jogging 1.446046541202e12 0.15388 -3.21831 -1.64837 2.3137520909090914 3.9336547272727276 5.702159909090909 2.3679054399999996e-2 10.357519256099998 2.7171236568999997 3.619160395367964 8.54849712858296 2.1598720909090914 7.151964727272727 7.350529909090909 2.2532978925619833 6.404875165289256 5.647020545454545 4.665047449088011 51.15059946015325 54.03028994444001 6.019592997461543 48.471210379402834 40.376039082987106 2.4534858869497382 6.962126857462656 6.354214277390015
user_005 Jogging 1.446046541243e12 6.28513 -19.38948 -19.12243 2.7805632727272727 -6.196841636363636 -5.783482818181818 39.5028591169 375.95193467039996 365.66732910490003 27.94856208988577 11.145794748966885 3.504566727272727 13.192638363636362 13.338947181818185 2.0841822975206616 9.427113429752067 9.935095214876032 12.281987945907073 174.04570699368992 177.9275119193353 5.80539289850129 97.95673045184817 113.73688837266178 2.409438295225941 9.897309253117646 10.664749803566036
user_005 Jogging 1.446046541291e12 11.38173 -14.1396 1.83878 5.1808084545454545 -11.328278181818183 -2.508836363636365 129.5437777929 199.92828816 3.3811118884000004 18.24426424499766 18.29774117897203 6.200921545454545 2.811321818181817 4.347616363636365 3.377254479338843 6.845085942148759 12.621001190082644 38.45142801288238 7.903530365385117 18.90176804535869 16.24475305624752 73.01666916174067 194.4489963055439 4.0304780183307685 8.544979178543425 13.94449699005109
user_005 Jogging 1.446046541388e12 -3.60151 -19.58108 -11.07517 -3.3402345454545452 -13.547373636363632 6.322252727272727 12.970874280100002 383.4186939664 122.6593905289 22.782646000309096 17.51251075208498 0.261275454545455 6.033706363636368 17.397422727272726 5.5190750413223135 4.820123553719009 5.400312809917355 6.82648631479341e-2 36.405612482586 302.67031755142557 35.255405054488655 29.324256254471905 50.695833226842296 5.937626213773368 5.415187554874891 7.120100647241041
user_005 Jogging 1.446046541436e12 12.14814 -11.45717 -4.25415 1.0073781818181815 -18.337410909090906 -5.93328090909091 147.57730545959998 131.2667444089 18.0977922225 17.23200052492455 22.84576654526576 11.140761818181819 6.880240909090906 1.67913090909091 7.029086033057851 5.398413305785124 9.654501570247934 124.11657388945787 47.33771496712806 2.8194806098644656 56.89371829485072 34.41505704101075 156.25215469199318 7.542792473272132 5.866434781109456 12.500086187382596
user_005 Jogging 1.446046541542e12 0.307161 -2.68182 -3.87095 -7.788874454545455 -1.243068181818182 -8.194178181818181 9.434787992100001e-2 7.192158512400001 14.9842539025 4.719190639804775 14.113925983821156 8.096035454545456 1.4387518181818182 4.32322818181818 10.823112314049588 4.726066363636364 2.2985858677685944 65.54579008125705 2.0700067943214875 18.69030191206693 164.5818232479703 64.88748743124589 7.553243462068892 12.828944744131151 8.055276992831836 2.74831647778579
user_005 Jogging 1.446046541696e12 5.13552 -19.58108 -3.44943 7.4800272727272725 -19.48353727272727 0.285061818181818 26.373565670399998 383.4186939664 11.8985673249 20.53511205135487 23.603902055517196 2.344507272727273 9.754272727273161e-2 3.734491818181818 10.172302371900825 5.747412975206613 4.432490809917356 5.496714351871075 9.5145836438025e-3 13.946429140066941 141.17685676629932 51.121567963913215 29.01355584951671 11.881786766572581 7.149934822354202 5.386423289114652
user_005 Jogging 1.44604654172e12 -7.66346 -17.70339 1.76214 8.159341999999999 -19.410380909090907 -1.2721369090909092 58.728619171599995 313.41001749209994 3.1051373796000004 19.371209927190918 23.13952318159967 15.822802 1.7069909090909086 3.0342769090909094 12.676106892561982 2.8030826446281014 3.9175418099173553 250.361063131204 2.9138179637190063 9.206836361042283 185.12551732456777 15.969343900020288 25.30357017118571 13.606083834982341 3.9961661502020016 5.030265417568511
user_005 Jogging 1.4460465418e12 -2.33694 10.07884 12.72175 -1.7795533636363636 5.564011818181817 11.467626363636365 5.461288563599999 101.5830157456 161.8429230625 16.397781172210465 18.88500083389981 0.5573866363636362 4.514828181818182 1.2541236363636354 5.894359570247934 14.68871404958678 6.774461652892561 0.31067986239676837 20.383673511339673 1.572826095285948 63.32538403099489 286.51145284843136 52.4522313273327 7.957724802416511 16.926649191391405 7.242391271350416
user_005 Jogging 1.446046541922e12 9.73396 -12.68342 -3.37279 4.647808181818181 -9.004675272727273 -10.085808545454546 94.7499772816 160.8691428964 11.375712384100002 16.33997651657125 15.640494555029901 5.086151818181818 3.6787447272727274 6.7130185454545455 3.0102033719008263 10.432625958677686 11.195548082644628 25.868940317594216 13.533162768436894 45.064617991616664 13.451884134769642 124.36908398090496 137.54178434293215 3.6676810295839033 11.152088772104756 11.727820954590506
user_005 Jogging 1.446046542092e12 5.86361 -18.92964 -16.32505 -1.162944727272727 -17.23309 -3.9615254545454546 34.3819222321 358.3312705296 266.5072575025 25.67528870848778 21.256831807594367 7.026554727272727 1.6965499999999984 12.363524545454545 3.595142479338843 4.947120743801654 9.631383471074379 49.37247133535871 2.8782819024999946 152.856739186057 16.645394279775534 28.83143743943179 146.05322223852409 4.079876748110847 5.369491357608446 12.085248124822431
user_005 Jogging 1.446046542181e12 -15.97897 -5.24928 -11.26677 1.3000036363636367 -3.256627272727273 -8.998904545454543 255.3274822609 27.5549405184 126.94010623289998 20.244073923304075 15.630175991661531 17.278973636363638 1.9926527272727266 2.267865454545456 10.113078115702478 8.66989082644628 3.8348817355371896 298.56292992614965 3.970664891507435 5.143213719920667 122.15093013029342 114.43345124093472 17.24598361886949 11.052191191356282 10.697357208251706 4.152828387842374
user_005 Jogging 1.446046542222e12 0.422122 -2.41358 -6.09353 -6.357091636363637 -1.2709399999999997 -7.211784636363637 0.178186982884 5.8253684164 37.1311078609 6.567698475126884 12.67392205058049 6.779213636363637 1.1426400000000003 1.1182546363636368 9.366308314049588 5.309105123966943 3.5045659752066105 45.95773752745868 1.3056261696000007 1.2504934317487695 118.53790978460839 63.76154511363488 15.934000527197712 10.887511643374182 7.985082661665744 3.99174154063082
user_005 Jogging 1.446046542424e12 -4.40624 -11.80206 6.09233 4.139191909090909 -18.246837272727273 -0.3245805454545451 19.414950937600004 139.2886202436 37.11648482889999 13.993571953225523 19.948414998235947 8.545431909090908 6.444777272727272 6.416910545454544 8.179328041322314 2.9753652892562 2.8794063636363636 73.02440651290908 41.535154095061976 41.17674094836574 79.82707085325661 14.223698002062362 13.350041030829283 8.934599647060669 3.77143182386509 3.6537707961541983
user_005 Jogging 1.446046542651e12 1.53341 -16.82202 19.08292 6.264227999999999 -17.29928 -3.9127539090909083 2.3513462280999997 282.98035688039994 364.15783572640004 25.48508463464267 24.160861800359214 4.730817999999999 0.47726000000000113 22.99567390909091 7.284976140495868 8.19864711570248 14.780556867768594 22.380638949123995 0.22777710760000108 528.8010185332445 56.60867013632807 109.01950719672978 257.7931864713368 7.523873346643208 10.441240692404795 16.055939289600495
user_005 Jogging 1.446046542667e12 -0.420925 -5.47921 9.96268 4.801088818181818 -15.47384090909091 1.4207360909090907 0.177177855625 30.021742224100002 99.25499278240001 11.377781543962119 21.644529400745 5.222013818181818 9.99463090909091 8.54194390909091 6.929325727272727 6.4564976942148755 13.418443363636364 27.269428317281847 99.8926470089554 72.9648057460553 51.89172275386088 62.058389545976496 219.45993950684507 7.203590962420123 7.877714741343234 14.814180352177608
user_005 Jogging 1.446046542675e12 -1.83878 -4.9044 6.39889 3.5400015454545466 -14.139597272727274 3.779177 3.3811118884000004 24.05313936 40.945793232099994 8.269222725292867 19.653619575324555 5.3787815454545465 9.235197272727273 2.619713 6.586026388429753 5.882959925619835 12.331539462809918 28.9312909137224 85.28886866618926 6.862896202369 46.90225966063993 47.84651938125171 200.77022596340439 6.848522443610733 6.917117852202007 14.169341056076123
user_005 Jogging 1.446046542739e12 1.07357 -19.58108 -14.63896 0.30367772727272724 -11.370084545454546 3.1137954545454547 1.1525525448999998 383.4186939664 214.29914988160002 24.471828627891707 14.200580585542609 0.7698922727272727 8.210995454545454 17.752755454545454 2.8844750495867775 6.841283471074382 6.838433719008266 0.5927341116051652 67.42044635456611 315.1603262288934 11.334512609664113 53.77129461838979 75.9497419307865 3.3666767901989214 7.332891286415597 8.714914912423787
user_005 Jogging 1.446046542861e12 -4.09967 2.14654 -2.2615 -0.7971601818181817 -5.395598454545454 -7.67162909090909 16.8072941089 4.607633971599999 5.114382249999999 5.15066115469655 10.56409483567436 3.302509818181818 7.542138454545454 5.41012909090909 1.284205123966942 7.828111231404958 4.942052809917355 10.906571099187305 56.883852467533295 29.26949678030082 2.4156453179541844 68.85564282404087 28.973992253594517 1.5542346405720677 8.297930032486468 5.382749506859344
user_005 Jogging 1.446046542942e12 0.307161 -1.76214 -4.17751 -3.141665909090909 2.9024918181818182 -3.5748390909090904 9.434787992100001e-2 3.1051373796000004 17.4515898001 4.544345393961709 6.196367795879178 3.4488269090909087 4.664631818181818 0.6026709090909095 2.230811289256198 4.1471462314049585 1.8555266115702478 11.894407048869551 21.758789999194217 0.3632122246644633 5.7556637291912045 21.774195531772843 5.234672484273779 2.3990964401605877 4.666282838810014 2.2879406645002356
user_005 Jogging 1.446046543055e12 9.12083 -19.58108 -7.51138 5.807868272727273 -19.180459090909086 -2.620314909090909 83.1895398889 383.4186939664 56.4208295044 22.869828669224873 22.320706230307078 3.312961727272727 0.4006209090909145 4.891065090909091 7.21340320661157 7.456624793388429 4.508180297520661 10.97571540637389 0.1604971128008308 23.922517723509557 70.92082738462611 81.22563714319311 25.297300130523492 8.421450432355824 9.012526679194526 5.029642147362324
user_005 Jogging 1.44604654333e12 3.44943 -19.58108 16.4005 2.7352753636363634 -13.958446363636364 -6.299065454545453 11.8985673249 383.4186939664 268.97640025000004 25.773894962564352 21.0075486111602 0.7141546363636366 5.622633636363636 22.699565454545453 3.6011598842975205 9.98418388429752 12.89937814876033 0.5100168446396781 31.614009008767763 515.2702718251934 18.185449279429097 109.58084417423078 215.4924638985187 4.264440089792457 10.468086939562108 14.679661573024042
user_005 Jogging 1.446046543339e12 4.98224 -19.58108 0.919089 2.4635499090909083 -15.49125909090909 -4.957854636363636 24.8227154176 383.4186939664 0.8447245899210001 20.225877829501517 21.37385900560983 2.5186900909090917 4.089820909090911 5.876943636363636 3.4383779917355373 9.535741305785121 12.211196347107439 6.3437997740436485 16.7266350684372 34.53846650499504 17.073977609871836 103.70063629752617 202.1941164653598 4.132066990002925 10.183350936579087 14.219497757141768
user_005 Jogging 1.446046543371e12 -2.10702 -19.58108 3.17999 -0.5742053636363637 -17.881052727272728 2.1383716363636363 4.439533280399999 383.4186939664 10.1123364001 19.949199574090684 19.746132967476807 1.5328146363636361 1.7000272727272723 1.0416183636363638 3.6401132148760342 5.236264876033058 7.928505719008263 2.349520709450586 2.8900927280165276 1.0849688154644963 17.808548436835352 36.04540436756053 138.59882739066543 4.220017587266119 6.003782505018027 11.772800320682647
user_005 Jogging 1.446046543403e12 1.45677 -19.35116 -12.2631 -6.367545454545442e-3 -19.312838181818176 0.7867098181818175 2.1221788328999995 374.4673933456 150.38362161 22.955896710616642 21.424840470675225 1.4631375454545454 3.832181818182434e-2 13.049809818181817 1.719979917355372 2.37902555371901 8.625239404958677 2.140771476918752 1.4685617487608027e-3 170.29753629071456 4.406007892590968 10.773255456819701 151.92967159914915 2.0990492830305265 3.2822637701470154 12.325975482660557
user_005 Jogging 1.446046543436e12 8.62267 -9.57948 -10.04052 1.533412818181818 -17.522235454545452 -6.330417363636363 74.35043792889999 91.7664370704 100.81204187040001 16.337959385116 20.2231033082854 7.089257181818182 7.942755454545452 3.7101026363636374 2.958264413223141 2.078480743801654 5.803152570247933 50.25756738996067 63.08736421071153 13.764861572352412 14.241782773955505 9.142709415267989 55.880129580603835 3.7738286625064874 3.0236913558212235 7.475301303666885
user_005 Jogging 1.446046543444e12 8.69931 -5.59417 -9.84892 2.5645773636363636 -16.39701181818182 -7.197850000000002 75.67799447610001 31.2947379889 97.00122516639999 14.281945162736061 19.86986137091605 6.134732636363637 10.80284181818182 2.651069999999998 3.1872362975206614 2.9557304958677695 5.917480165289256 37.63494451966514 116.70139134865789 7.028172144899989 16.474435994988536 19.63105162598625 56.34253170650897 4.058871271054126 4.430694260043932 7.506166245594949
user_005 Jogging 1.446046543508e12 -0.919089 2.56806 -5.0972 4.104354909090909 -2.929164636363637 -8.281270909090908 0.8447245899210001 6.5949321636 25.98144784 5.781098908816645 10.802467948038467 5.0234439090909095 5.497224636363637 3.1840709090909085 4.073036859504132 8.464671801652893 2.309668578512397 25.23498870778256 30.219478702643315 10.138307554119004 20.73373618005687 76.00364634040206 6.9007059023571315 4.553431253467748 8.718007016537785 2.6269194700936556
user_005 Jogging 1.446046543541e12 -3.83143 1.18853 -0.881966 0.17478127272727265 0.7983571818181816 -5.821804181818181 14.6798558449 1.4126035609000003 0.7778640251560001 4.107349927989579 6.9965167402069 4.006211272727273 0.3901728181818185 4.939838181818181 3.644546297520661 6.136317785123967 2.6650025619834707 16.049728761727078 0.1522348280479424 24.40200126254875 15.574869901198497 49.55435757769464 8.901935284719384 3.946500969364951 7.039485604623014 2.983611114860545
user_005 Jogging 1.446046543581e12 -1.83878 -1.11069 -0.537083 -2.3996464545454548 0.9272535454545455 -2.376459090909091 3.3811118884000004 1.2336322760999998 0.28845814888899995 2.2143175728402196 4.207773037473346 0.5608664545454547 2.0379435454545454 1.839376090909091 3.172033743801653 2.5851962644628106 3.4196922975206614 0.3145711798343886 4.153213894459842 3.3833044038080087 13.604792506818278 10.39215341495098 12.482257721226553 3.6884675011199812 3.2236863083977294 3.5330238778172096
user_005 Jogging 1.446046543768e12 -2.10702 -1.22565 7.39522 0.8436457272727271 -7.370835454545454 0.8041268181818185 4.439533280399999 1.5022179224999999 54.6892788484 7.786592968127973 9.637813049839506 2.9506657272727272 6.145185454545454 6.591093181818182 2.724542628099174 7.275158842975207 4.76882152892562 8.706428234101892 37.76330427075702 43.44250933141012 9.235165670215759 61.3999239324024 28.268622903381537 3.038941537808149 7.835810355821687 5.316824513126377
user_005 Jogging 1.446046543776e12 -1.14901 -1.8771 6.39889 0.8297110909090908 -5.761382727272728 1.9537359090909092 1.3202239801000002 3.52350441 40.945793232099994 6.766795520938992 8.382296009008487 1.9787210909090909 3.8842827272727276 4.4451540909090905 2.794532537190083 7.244439008264464 4.54301652892562 3.9153371556084626 15.087652305389259 19.759394891925822 9.458262227633652 61.15089409500795 25.700279986111074 3.075428787605665 7.819903713921799 5.069544356854083
user_005 Jogging 1.446046543899e12 8.08618 -19.58108 -0.345482 8.922263636363637 -3.0336731818181817 -8.249916545454546 65.38630699240001 383.4186939664 0.119357812324 21.18783516008948 14.782951570206615 0.8360836363636359 16.54740681818182 7.904434545454547 4.691229611570248 4.17659847107438 7.8366609090909085 0.6990358469950406 273.8166724064102 62.48008548337523 27.402560312610817 41.6009787463552 78.44553029380619 5.234745486899131 6.4498820722828105 8.856948136565224
user_005 Jogging 1.446046543931e12 -6.51385 -19.58108 -5.32712 4.299441818181818 -9.520255818181818 -5.097199272727273 42.430241822499994 383.4186939664 28.378207494399998 21.312605267383432 19.3627663237903 10.813291818181817 10.060824181818182 0.22992072727272728 7.600088487603307 8.318992033057851 8.151140826446282 116.92727994515782 101.22018321745749 5.286354082961984e-2 73.86016063086305 98.25547117025539 110.92824713448081 8.594193425264702 9.912389780989011 10.532247962067776
user_005 Jogging 1.44604654398e12 9.46572 -16.89866 -4.25415 -0.7205188181818183 -17.67899909090909 1.4381556363636365 89.59985511839999 285.5647097956 18.0977922225 19.83084358106079 19.670062757952863 10.186238818181817 0.7803390909090915 5.692305636363637 7.83032711570248 8.036180578512397 6.404241578512397 103.75946126103409 0.6089290968008273 32.40234345777723 81.04664685578355 93.61057053591657 85.36081290888455 9.002591118993662 9.675255579875737 9.239091562966813
user_005 Jogging 1.446046544255e12 -5.17264 0.498763 3.63983 -4.434106363636364 -1.9572211818181822 -0.43257227272727294 26.756204569600005 0.24876453016900002 13.248362428899998 6.344551326033151 6.585032182207585 0.7385336363636368 2.4559841818181822 4.072402272727273 1.7532333884297522 4.769137553719007 3.826648140495868 0.5454319320404964 6.031858301341126 16.58446027091426 3.4661914932591844 24.218586942638918 19.63088592880002 1.8617710636002442 4.921238354585045 4.430675561220887
user_005 Jogging 1.446046544352e12 -5.70913 -19.58108 -6.09353 -1.7203315454545456 -11.558200000000001 -3.216022363636364 32.5941653569 383.4186939664 37.1311078609 21.287178469308703 12.672935690213166 3.9887984545454547 8.022879999999999 2.8775076363636365 2.8122678677685955 6.869153115702479 2.6387184628099174 15.910513110984208 64.36660349439998 8.280050197331041 9.862269849087586 58.872521967012815 8.851188233063542 3.14042510642868 7.6728431475570265 2.9750946595131293
user_005 Jogging 1.446046544392e12 3.60271 -19.58108 -6.47673 -1.1733964545454543 -18.02736545454545 -6.616078181818182 12.9795193441 383.4186939664 41.9480314929 20.936720010627262 19.676679123590134 4.776106454545454 1.5537145454545502 0.13934818181818187 2.5677780578512395 6.881187867768597 3.4491445454545455 22.811192865150748 2.4140288887570396 1.9417915776033072e-2 8.397670316512064 57.70691056056415 18.3672542259302 2.897873412782564 7.596506470777482 4.285703469202017
user_005 Jogging 1.446046544457e12 2.72134 -2.49022 2.4519 4.543298181818181 -13.223392727272726 -3.0174525454545456 7.405691395600001 6.2011956484 6.011813610000001 4.429300244282386 15.021875104562008 1.821958181818181 10.733172727272727 5.469352545454546 3.766792727272727 5.418364876033059 4.356480776859505 3.3195316162942117 115.20099679347108 29.913817266470122 17.912531199467377 44.40494266927388 24.473405190686368 4.23231983662239 6.663703374946538 4.947060257434345
user_005 Jogging 1.446046544611e12 -0.689167 -1.07237 -2.29982 1.8434560909090907 -0.21538854545454544 -0.4499924545454545 0.47495115388899994 1.1499774169 5.2891720324 2.629467741423918 2.762459505633797 2.5326230909090905 0.8569814545454546 1.8498275454545454 1.3595797438016528 1.0650511983471072 2.122819520661157 6.414179720605915 0.7344172134348431 3.4218619479223884 2.1293145833974765 1.1827212289184335 4.709658674995932 1.4592171131800356 1.0875298749544462 2.170174802866334
user_005 Jogging 1.446046544821e12 5.40376 -16.93698 -9.12083 0.4116704545454546 -18.992341818181817 -3.8605 29.2006221376 286.86129152039996 83.1895398889 19.981277575442967 20.556470047062273 4.9920895454545455 2.0553618181818187 5.26033 4.955671487603306 0.8905509917355384 3.986896099173553 24.92095802983657 4.224512203639672 27.671071708899998 29.33488107108366 1.1913207005563502 20.324670741318293 5.416168486216401 1.0914763857071532 4.508289114655169
  1. Prediction using Random Forests

Instead of just stopping at ETL and feature engineering let's quickly see without understanding the random forest model in detail how simple it is to predict the activity using random forest model.

val splits = dataFeatDF.randomSplit(Array(0.7, 0.3))
val (trainingData, testData) = (splits(0), splits(1))
splits: Array[org.apache.spark.sql.Dataset[org.apache.spark.sql.Row]] = Array([user_id: string, activity: string ... 27 more fields], [user_id: string, activity: string ... 27 more fields])
trainingData: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [user_id: string, activity: string ... 27 more fields]
testData: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [user_id: string, activity: string ... 27 more fields]
import org.apache.spark.ml.feature.{StringIndexer,VectorAssembler}
import org.apache.spark.ml.Pipeline

import org.apache.spark.ml.classification.RandomForestClassifier

val transformers = Array(
              new StringIndexer().setInputCol("activity").setOutputCol("label"),
              new VectorAssembler()
                      .setInputCols(Array("meanX", "meanY", "meanZ", "stddevX", "stddevY","stddevZ"))
                      .setOutputCol("features")
)

// Train a RandomForest model.
val rf = new RandomForestClassifier() 
              .setLabelCol("label")
              .setFeaturesCol("features")
              .setNumTrees(10)
              .setFeatureSubsetStrategy("auto")
              .setImpurity("gini")
              .setMaxDepth(20)
              .setMaxBins(32)
              .setSeed(12345)

val model = new Pipeline().setStages(transformers :+ rf).fit(trainingData)
import org.apache.spark.ml.feature.{StringIndexer, VectorAssembler}
import org.apache.spark.ml.Pipeline
import org.apache.spark.ml.classification.RandomForestClassifier
transformers: Array[org.apache.spark.ml.PipelineStage with org.apache.spark.ml.param.shared.HasOutputCol with org.apache.spark.ml.param.shared.HasInputCols with org.apache.spark.ml.param.shared.HasHandleInvalid with org.apache.spark.ml.util.DefaultParamsWritable{def copy(extra: org.apache.spark.ml.param.ParamMap): org.apache.spark.ml.PipelineStage with org.apache.spark.ml.param.shared.HasOutputCol with org.apache.spark.ml.param.shared.HasInputCols with org.apache.spark.ml.param.shared.HasHandleInvalid with org.apache.spark.ml.util.DefaultParamsWritable{def copy(extra: org.apache.spark.ml.param.ParamMap): org.apache.spark.ml.PipelineStage with org.apache.spark.ml.param.shared.HasOutputCol with org.apache.spark.ml.param.shared.HasInputCols with org.apache.spark.ml.param.shared.HasHandleInvalid with org.apache.spark.ml.util.DefaultParamsWritable}}] = Array(strIdx_d760fa44cad2, VectorAssembler: uid=vecAssembler_3d7b1fc4476e, handleInvalid=error, numInputCols=6)
rf: org.apache.spark.ml.classification.RandomForestClassifier = rfc_794232dabcdf
model: org.apache.spark.ml.PipelineModel = pipeline_76d41a70ccc7

Before we go further let's find quickly which label is mapped to which activity by the StringIndexer and quickly check that the estimator we have built can transform the union of the training and test data. This is mostly for debugging... not something you would do in a real pipeline except during debugging stages.

val activityLabelDF = model.transform(trainingData.union(testData)).select("activity","label").distinct
display(activityLabelDF) // this just shows what activity is associated with what label
activity label
Jogging 0.0
Jumping 4.0
Standing 1.0
Walking 2.0
Sitting 3.0
val myPredictionsOnTestData = model.transform(testData)
display(myPredictionsOnTestData)

Let's evaluate accuracy at a lower level...

val accuracy: Double = 1.0 * model.transform(testData)
                                  .select("activity","label","prediction")
                                  .filter($"label"===$"prediction").count() / testData.count() 
accuracy: Double = 0.9850159665929747

We get 98% correct predictions and here are the mis-predicted ones.

display(model.transform(testData).select("activity","label","prediction").filter(not($"label"===$"prediction")))
activity label prediction
Jogging 0.0 4.0
Jogging 0.0 4.0
Jogging 0.0 4.0
Jogging 0.0 4.0
Jogging 0.0 4.0
Jogging 0.0 4.0
Jogging 0.0 4.0
Jogging 0.0 4.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Walking 2.0 0.0
Jogging 0.0 2.0
Jumping 4.0 0.0
Standing 1.0 2.0
Standing 1.0 2.0
Standing 1.0 2.0
Standing 1.0 2.0
Standing 1.0 2.0
Standing 1.0 2.0
Standing 1.0 2.0
Walking 2.0 1.0
Walking 2.0 1.0
Jumping 4.0 2.0
Jumping 4.0 2.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Walking 2.0 1.0
Walking 2.0 1.0
Walking 2.0 1.0
Jogging 0.0 4.0
Jogging 0.0 4.0
Jogging 0.0 4.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 1.0
Walking 2.0 0.0
Jogging 0.0 4.0
Jogging 0.0 2.0
Jogging 0.0 4.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Standing 1.0 2.0
Jogging 0.0 2.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
testData.printSchema()
root
 |-- user_id: string (nullable = true)
 |-- activity: string (nullable = true)
 |-- timeStampAsLong: long (nullable = true)
 |-- x: double (nullable = true)
 |-- y: double (nullable = true)
 |-- z: double (nullable = true)
 |-- meanX: double (nullable = true)
 |-- meanY: double (nullable = true)
 |-- meanZ: double (nullable = true)
 |-- SqX: double (nullable = true)
 |-- SqY: double (nullable = true)
 |-- SqZ: double (nullable = true)
 |-- resultant: double (nullable = true)
 |-- meanResultant: double (nullable = true)
 |-- absDevFromMeanX: double (nullable = true)
 |-- absDevFromMeanY: double (nullable = true)
 |-- absDevFromMeanZ: double (nullable = true)
 |-- meanAbsDevFromMeanX: double (nullable = true)
 |-- meanAbsDevFromMeanY: double (nullable = true)
 |-- meanAbsDevFromMeanZ: double (nullable = true)
 |-- sqrDevFromMeanX: double (nullable = true)
 |-- sqrDevFromMeanY: double (nullable = true)
 |-- sqrDevFromMeanZ: double (nullable = true)
 |-- varianceX: double (nullable = true)
 |-- varianceY: double (nullable = true)
 |-- varianceZ: double (nullable = true)
 |-- stddevX: double (nullable = true)
 |-- stddevY: double (nullable = true)
 |-- stddevZ: double (nullable = true)

Let's understand the mis-predicitons better by seeing the user_id also.

display(model.transform(testData).select("user_id","activity","label","prediction").filter(not($"label"===$"prediction")))
user_id activity label prediction
user_001 Jogging 0.0 4.0
user_001 Jogging 0.0 4.0
user_001 Jogging 0.0 4.0
user_001 Jogging 0.0 4.0
user_001 Jogging 0.0 4.0
user_001 Jogging 0.0 4.0
user_001 Jogging 0.0 4.0
user_001 Jogging 0.0 4.0
user_001 Jumping 4.0 0.0
user_001 Jumping 4.0 0.0
user_001 Jumping 4.0 0.0
user_001 Walking 2.0 0.0
user_002 Jogging 0.0 2.0
user_002 Jumping 4.0 0.0
user_002 Standing 1.0 2.0
user_002 Standing 1.0 2.0
user_002 Standing 1.0 2.0
user_002 Standing 1.0 2.0
user_002 Standing 1.0 2.0
user_002 Standing 1.0 2.0
user_002 Standing 1.0 2.0
user_002 Walking 2.0 1.0
user_002 Walking 2.0 1.0
user_003 Jumping 4.0 2.0
user_003 Jumping 4.0 2.0
user_003 Jumping 4.0 0.0
user_003 Jumping 4.0 0.0
user_003 Walking 2.0 1.0
user_003 Walking 2.0 1.0
user_003 Walking 2.0 1.0
user_004 Jogging 0.0 4.0
user_004 Jogging 0.0 4.0
user_004 Jogging 0.0 4.0
user_004 Jumping 4.0 0.0
user_004 Jumping 4.0 0.0
user_004 Jumping 4.0 0.0
user_004 Jumping 4.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 1.0
user_004 Walking 2.0 0.0
user_005 Jogging 0.0 4.0
user_005 Jogging 0.0 2.0
user_005 Jogging 0.0 4.0
user_005 Jumping 4.0 0.0
user_005 Jumping 4.0 0.0
user_005 Jumping 4.0 0.0
user_005 Standing 1.0 2.0
user_006 Jogging 0.0 2.0
user_006 Walking 2.0 0.0
user_006 Walking 2.0 0.0
user_007 Walking 2.0 0.0

Let's evaluate our model's accuracy using ML pipeline's evaluation.MulticlassClassificationEvaluator:

import org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator

// Select (prediction, true label) and compute test error.
val evaluator = new MulticlassClassificationEvaluator()
  .setLabelCol("label")
  .setPredictionCol("prediction")
  .setMetricName("accuracy")
val accuracy = evaluator.evaluate(myPredictionsOnTestData)
println(s"Test Error = ${(1.0 - accuracy)}")
Test Error = 0.014984033407025255
import org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator
evaluator: org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator = MulticlassClassificationEvaluator: uid=mcEval_656aec85ac9d, metricName=accuracy, metricLabel=0.0, beta=1.0, eps=1.0E-15
accuracy: Double = 0.9850159665929747

Note, it's the same 98% we got from our slightly lower-level operations earlier for accuracy.

Think!

What else do you need to investigate to try to understand the mis-predicitons better?

  • time-line?
  • are mis-predictions happening during transitions between users or activities of the same user or both, as our Markov process simply uses the same sliding window over the time-odered, user-grouped, activity streams...
  • ...

Typically, in inustry you will have to improve on an existing algorithm that is in production and getting into the details under the given constraints needs some thinking from scratch over the entire data science pipeline and process.

Explaining the Model's Predictions to a Curious Client whose Activity is being Predicted

Now, let's try to explain the decision branches in each tree of our best-fitted random forest model. Often, being able to "explain" why the model "predicts" is critical for various businesses. how it predicts.

import org.apache.spark.ml.classification.RandomForestClassificationModel
val rfModel = model.stages(2).asInstanceOf[RandomForestClassificationModel]
println(s"Learned classification forest model:\n ${rfModel.toDebugString}")
Learned classification forest model:
 RandomForestClassificationModel: uid=rfc_794232dabcdf, numTrees=10, numClasses=5, numFeatures=6
  Tree 0 (weight 1.0):
    If (feature 3 <= 0.5225058552059478)
     If (feature 1 <= -8.168595136363637)
      If (feature 1 <= -10.122931363636361)
       If (feature 0 <= -8.90539)
        Predict: 0.0
       Else (feature 0 > -8.90539)
        Predict: 2.0
      Else (feature 1 > -10.122931363636361)
       If (feature 5 <= 0.80494691075511)
        If (feature 4 <= 0.9240406048221913)
         If (feature 5 <= 0.4040864257583746)
          If (feature 5 <= 0.029334843391680826)
           If (feature 1 <= -9.513290454545455)
            Predict: 2.0
           Else (feature 1 > -9.513290454545455)
            Predict: 1.0
          Else (feature 5 > 0.029334843391680826)
           Predict: 1.0
         Else (feature 5 > 0.4040864257583746)
          If (feature 2 <= -1.21523575)
           Predict: 2.0
          Else (feature 2 > -1.21523575)
           Predict: 1.0
        Else (feature 4 > 0.9240406048221913)
         If (feature 1 <= -9.419232727272725)
          Predict: 1.0
         Else (feature 1 > -9.419232727272725)
          Predict: 2.0
       Else (feature 5 > 0.80494691075511)
        Predict: 2.0
     Else (feature 1 > -8.168595136363637)
      If (feature 1 <= 3.231696363636363)
       If (feature 0 <= -2.5738281818181816)
        If (feature 3 <= 0.02774026246959616)
         Predict: 4.0
        Else (feature 3 > 0.02774026246959616)
         Predict: 0.0
       Else (feature 0 > -2.5738281818181816)
        If (feature 1 <= -4.157154727272728)
         If (feature 4 <= 0.02938177926107125)
          Predict: 4.0
         Else (feature 4 > 0.02938177926107125)
          Predict: 2.0
        Else (feature 1 > -4.157154727272728)
         Predict: 3.0
      Else (feature 1 > 3.231696363636363)
       If (feature 3 <= 0.07730407812363697)
        If (feature 0 <= -3.7931120454545457)
         Predict: 0.0
        Else (feature 0 > -3.7931120454545457)
         Predict: 3.0
       Else (feature 3 > 0.07730407812363697)
        If (feature 0 <= 0.32806340909090914)
         If (feature 4 <= 0.9240406048221913)
          Predict: 2.0
         Else (feature 4 > 0.9240406048221913)
          Predict: 3.0
        Else (feature 0 > 0.32806340909090914)
         Predict: 4.0
    Else (feature 3 > 0.5225058552059478)
     If (feature 4 <= 3.509467511028114)
      If (feature 5 <= 2.5963437348657123)
       If (feature 3 <= 3.2533446617122705)
        If (feature 5 <= 0.80494691075511)
         If (feature 2 <= 2.8699414545454545)
          If (feature 0 <= 2.8798476363636363)
           If (feature 0 <= -5.7328163636363625)
            If (feature 0 <= -8.90539)
             If (feature 3 <= 2.499281243538517)
              Predict: 4.0
             Else (feature 3 > 2.499281243538517)
              Predict: 0.0
            Else (feature 0 > -8.90539)
             Predict: 0.0
           Else (feature 0 > -5.7328163636363625)
            If (feature 3 <= 1.6040286540977868)
             If (feature 1 <= -8.617986363636366)
              If (feature 4 <= 1.9631927695493916)
               If (feature 0 <= -2.5738281818181816)
                If (feature 2 <= -0.38031795454545453)
                 Predict: 1.0
                Else (feature 2 > -0.38031795454545453)
                 Predict: 2.0
               Else (feature 0 > -2.5738281818181816)
                Predict: 1.0
              Else (feature 4 > 1.9631927695493916)
               Predict: 0.0
             Else (feature 1 > -8.617986363636366)
              If (feature 2 <= -1.073567681818182)
               Predict: 1.0
              Else (feature 2 > -1.073567681818182)
               If (feature 3 <= 1.1186607583073207)
                Predict: 2.0
               Else (feature 3 > 1.1186607583073207)
                Predict: 1.0
            Else (feature 3 > 1.6040286540977868)
             If (feature 2 <= -0.5214064090909091)
              If (feature 3 <= 1.8104608428061633)
               Predict: 2.0
              Else (feature 3 > 1.8104608428061633)
               Predict: 4.0
             Else (feature 2 > -0.5214064090909091)
              Predict: 2.0
          Else (feature 0 > 2.8798476363636363)
           If (feature 4 <= 0.9240406048221913)
            Predict: 1.0
           Else (feature 4 > 0.9240406048221913)
            Predict: 2.0
         Else (feature 2 > 2.8699414545454545)
          Predict: 2.0
        Else (feature 5 > 0.80494691075511)
         If (feature 1 <= -13.949734999999999)
          If (feature 2 <= -0.04588640909090911)
           If (feature 5 <= 1.468512909467716)
            Predict: 0.0
           Else (feature 5 > 1.468512909467716)
            If (feature 0 <= -0.5881405909090909)
             Predict: 2.0
            Else (feature 0 > -0.5881405909090909)
             Predict: 0.0
          Else (feature 2 > -0.04588640909090911)
           Predict: 0.0
         Else (feature 1 > -13.949734999999999)
          If (feature 0 <= -8.90539)
           Predict: 0.0
          Else (feature 0 > -8.90539)
           If (feature 1 <= -2.4344832727272725)
            If (feature 0 <= -0.5881405909090909)
             If (feature 1 <= -4.157154727272728)
              If (feature 4 <= 0.9240406048221913)
               If (feature 3 <= 2.29340842981981)
                If (feature 2 <= -0.6868815000000001)
                 If (feature 0 <= -4.420172227272728)
                  Predict: 1.0
                 Else (feature 0 > -4.420172227272728)
                  Predict: 2.0
                Else (feature 2 > -0.6868815000000001)
                 Predict: 2.0
               Else (feature 3 > 2.29340842981981)
                If (feature 2 <= -0.1991675454545455)
                 Predict: 2.0
                Else (feature 2 > -0.1991675454545455)
                 Predict: 1.0
              Else (feature 4 > 0.9240406048221913)
               Predict: 2.0
             Else (feature 1 > -4.157154727272728)
              If (feature 4 <= 2.258741828976616)
               Predict: 2.0
              Else (feature 4 > 2.258741828976616)
               Predict: 0.0
            Else (feature 0 > -0.5881405909090909)
             If (feature 4 <= 0.3869983835216714)
              Predict: 1.0
             Else (feature 4 > 0.3869983835216714)
              If (feature 4 <= 1.3210859432345212)
               If (feature 3 <= 1.1186607583073207)
                If (feature 4 <= 0.9240406048221913)
                 If (feature 0 <= -0.16835886363636363)
                  Predict: 2.0
                 Else (feature 0 > -0.16835886363636363)
                  Predict: 1.0
                Else (feature 4 > 0.9240406048221913)
                 Predict: 1.0
               Else (feature 3 > 1.1186607583073207)
                If (feature 5 <= 1.076775279931446)
                 If (feature 1 <= -9.2781435)
                  Predict: 2.0
                 Else (feature 1 > -9.2781435)
                  Predict: 1.0
                Else (feature 5 > 1.076775279931446)
                 If (feature 2 <= 0.6160089999999999)
                  Predict: 2.0
                 Else (feature 2 > 0.6160089999999999)
                  Predict: 1.0
              Else (feature 4 > 1.3210859432345212)
               Predict: 2.0
           Else (feature 1 > -2.4344832727272725)
            If (feature 1 <= 3.231696363636363)
             If (feature 1 <= 1.3574864545454546)
              Predict: 0.0
             Else (feature 1 > 1.3574864545454546)
              If (feature 4 <= 2.258741828976616)
               Predict: 4.0
              Else (feature 4 > 2.258741828976616)
               Predict: 0.0
            Else (feature 1 > 3.231696363636363)
             If (feature 4 <= 1.6647103963937675)
              Predict: 2.0
             Else (feature 4 > 1.6647103963937675)
              If (feature 2 <= 0.6160089999999999)
               Predict: 0.0
              Else (feature 2 > 0.6160089999999999)
               Predict: 2.0
       Else (feature 3 > 3.2533446617122705)
        If (feature 4 <= 0.3869983835216714)
         Predict: 1.0
        Else (feature 4 > 0.3869983835216714)
         If (feature 1 <= -6.928410727272727)
          If (feature 2 <= -1.21523575)
           If (feature 0 <= -7.16007390909091)
            If (feature 1 <= -7.391737681818182)
             Predict: 0.0
            Else (feature 1 > -7.391737681818182)
             Predict: 2.0
           Else (feature 0 > -7.16007390909091)
            If (feature 5 <= 1.468512909467716)
             Predict: 1.0
            Else (feature 5 > 1.468512909467716)
             Predict: 0.0
          Else (feature 2 > -1.21523575)
           If (feature 0 <= -8.90539)
            Predict: 0.0
           Else (feature 0 > -8.90539)
            If (feature 1 <= -17.560554999999994)
             Predict: 0.0
            Else (feature 1 > -17.560554999999994)
             If (feature 0 <= 3.5434871363636367)
              If (feature 4 <= 2.884105112415355)
               Predict: 2.0
              Else (feature 4 > 2.884105112415355)
               If (feature 5 <= 1.2763838461753882)
                Predict: 0.0
               Else (feature 5 > 1.2763838461753882)
                Predict: 2.0
             Else (feature 0 > 3.5434871363636367)
              Predict: 0.0
         Else (feature 1 > -6.928410727272727)
          If (feature 1 <= 1.3574864545454546)
           Predict: 0.0
          Else (feature 1 > 1.3574864545454546)
           If (feature 0 <= -3.125991409090909)
            If (feature 0 <= -5.033296227272727)
             Predict: 0.0
            Else (feature 0 > -5.033296227272727)
             Predict: 2.0
           Else (feature 0 > -3.125991409090909)
            Predict: 0.0
      Else (feature 5 > 2.5963437348657123)
       If (feature 0 <= 1.2947807727272727)
        If (feature 2 <= -2.184857272727273)
         If (feature 3 <= 2.29340842981981)
          If (feature 2 <= -2.8084323636363635)
           If (feature 0 <= -0.3738945909090909)
            Predict: 2.0
           Else (feature 0 > -0.3738945909090909)
            If (feature 4 <= 1.6647103963937675)
             Predict: 0.0
            Else (feature 4 > 1.6647103963937675)
             Predict: 2.0
          Else (feature 2 > -2.8084323636363635)
           If (feature 5 <= 3.803765702041731)
            Predict: 4.0
           Else (feature 5 > 3.803765702041731)
            Predict: 0.0
         Else (feature 3 > 2.29340842981981)
          Predict: 0.0
        Else (feature 2 > -2.184857272727273)
         If (feature 3 <= 3.6472443306163704)
          If (feature 3 <= 1.3680974461096451)
           If (feature 0 <= -1.488667)
            Predict: 0.0
           Else (feature 0 > -1.488667)
            Predict: 3.0
          Else (feature 3 > 1.3680974461096451)
           If (feature 0 <= -8.90539)
            Predict: 0.0
           Else (feature 0 > -8.90539)
            If (feature 1 <= -1.2012645454545452)
             If (feature 5 <= 5.9923123904255196)
              Predict: 2.0
             Else (feature 5 > 5.9923123904255196)
              Predict: 0.0
            Else (feature 1 > -1.2012645454545452)
             If (feature 0 <= -5.033296227272727)
              Predict: 2.0
             Else (feature 0 > -5.033296227272727)
              If (feature 3 <= 2.06138891346951)
               Predict: 2.0
              Else (feature 3 > 2.06138891346951)
               Predict: 0.0
         Else (feature 3 > 3.6472443306163704)
          If (feature 5 <= 2.815074767092767)
           If (feature 4 <= 2.258741828976616)
            Predict: 0.0
           Else (feature 4 > 2.258741828976616)
            If (feature 1 <= -8.71901181818182)
             Predict: 2.0
            Else (feature 1 > -8.71901181818182)
             Predict: 0.0
          Else (feature 5 > 2.815074767092767)
           Predict: 0.0
       Else (feature 0 > 1.2947807727272727)
        If (feature 5 <= 2.815074767092767)
         If (feature 0 <= 2.0507363636363634)
          If (feature 1 <= -9.513290454545455)
           Predict: 2.0
          Else (feature 1 > -9.513290454545455)
           Predict: 0.0
         Else (feature 0 > 2.0507363636363634)
          Predict: 0.0
        Else (feature 5 > 2.815074767092767)
         Predict: 0.0
     Else (feature 4 > 3.509467511028114)
      If (feature 4 <= 5.856212462090488)
       If (feature 3 <= 3.2533446617122705)
        If (feature 1 <= -8.168595136363637)
         If (feature 0 <= -2.0286351363636363)
          If (feature 3 <= 1.6040286540977868)
           Predict: 4.0
          Else (feature 3 > 1.6040286540977868)
           If (feature 5 <= 4.209746983589046)
            If (feature 0 <= -8.90539)
             Predict: 0.0
            Else (feature 0 > -8.90539)
             If (feature 1 <= -13.949734999999999)
              Predict: 4.0
             Else (feature 1 > -13.949734999999999)
              If (feature 4 <= 5.395001662922967)
               Predict: 0.0
              Else (feature 4 > 5.395001662922967)
               If (feature 0 <= -3.125991409090909)
                Predict: 0.0
               Else (feature 0 > -3.125991409090909)
                Predict: 4.0
           Else (feature 5 > 4.209746983589046)
            Predict: 2.0
         Else (feature 0 > -2.0286351363636363)
          If (feature 0 <= 2.8798476363636363)
           If (feature 1 <= -11.699289545454546)
            Predict: 0.0
           Else (feature 1 > -11.699289545454546)
            If (feature 5 <= 0.1803188998830109)
             Predict: 1.0
            Else (feature 5 > 0.1803188998830109)
             If (feature 2 <= 1.0950141818181818)
              If (feature 5 <= 4.852637451173388)
               If (feature 0 <= -1.488667)
                If (feature 1 <= -9.102216772727274)
                 Predict: 2.0
                Else (feature 1 > -9.102216772727274)
                 If (feature 1 <= -8.71901181818182)
                  Predict: 0.0
                 Else (feature 1 > -8.71901181818182)
                  Predict: 4.0
               Else (feature 0 > -1.488667)
                Predict: 2.0
              Else (feature 5 > 4.852637451173388)
               Predict: 4.0
             Else (feature 2 > 1.0950141818181818)
              Predict: 0.0
          Else (feature 0 > 2.8798476363636363)
           Predict: 0.0
        Else (feature 1 > -8.168595136363637)
         If (feature 3 <= 1.6040286540977868)
          If (feature 1 <= -6.928410727272727)
           Predict: 4.0
          Else (feature 1 > -6.928410727272727)
           If (feature 4 <= 3.987483559659423)
            If (feature 0 <= -1.488667)
             Predict: 0.0
            Else (feature 0 > -1.488667)
             Predict: 4.0
           Else (feature 4 > 3.987483559659423)
            Predict: 0.0
         Else (feature 3 > 1.6040286540977868)
          If (feature 1 <= -7.811519545454546)
           If (feature 4 <= 4.517274572453781)
            Predict: 2.0
           Else (feature 4 > 4.517274572453781)
            If (feature 3 <= 2.499281243538517)
             Predict: 2.0
            Else (feature 3 > 2.499281243538517)
             If (feature 5 <= 2.041048981215627)
              Predict: 0.0
             Else (feature 5 > 2.041048981215627)
              Predict: 2.0
          Else (feature 1 > -7.811519545454546)
           If (feature 2 <= 1.0950141818181818)
            If (feature 0 <= 0.32806340909090914)
             If (feature 3 <= 1.8104608428061633)
              If (feature 4 <= 5.01193131655486)
               Predict: 0.0
              Else (feature 4 > 5.01193131655486)
               Predict: 4.0
             Else (feature 3 > 1.8104608428061633)
              Predict: 0.0
            Else (feature 0 > 0.32806340909090914)
             If (feature 5 <= 1.763631215969657)
              If (feature 4 <= 4.517274572453781)
               Predict: 0.0
              Else (feature 4 > 4.517274572453781)
               Predict: 4.0
             Else (feature 5 > 1.763631215969657)
              If (feature 0 <= 0.9951855113636363)
               If (feature 5 <= 2.815074767092767)
                Predict: 2.0
               Else (feature 5 > 2.815074767092767)
                Predict: 0.0
              Else (feature 0 > 0.9951855113636363)
               Predict: 0.0
           Else (feature 2 > 1.0950141818181818)
            If (feature 3 <= 2.713415564122834)
             Predict: 0.0
            Else (feature 3 > 2.713415564122834)
             Predict: 2.0
       Else (feature 3 > 3.2533446617122705)
        If (feature 2 <= -1.21523575)
         If (feature 0 <= 2.8798476363636363)
          If (feature 5 <= 3.803765702041731)
           If (feature 0 <= -1.2779045454545455)
            Predict: 0.0
           Else (feature 0 > -1.2779045454545455)
            If (feature 0 <= -0.7518725909090909)
             Predict: 2.0
            Else (feature 0 > -0.7518725909090909)
             Predict: 0.0
          Else (feature 5 > 3.803765702041731)
           If (feature 2 <= -1.7981704545454544)
            Predict: 0.0
           Else (feature 2 > -1.7981704545454544)
            If (feature 1 <= -7.391737681818182)
             If (feature 5 <= 4.852637451173388)
              Predict: 2.0
             Else (feature 5 > 4.852637451173388)
              Predict: 0.0
            Else (feature 1 > -7.391737681818182)
             Predict: 0.0
         Else (feature 0 > 2.8798476363636363)
          If (feature 2 <= -1.7981704545454544)
           Predict: 0.0
          Else (feature 2 > -1.7981704545454544)
           If (feature 1 <= -13.949734999999999)
            Predict: 0.0
           Else (feature 1 > -13.949734999999999)
            If (feature 3 <= 5.04993896073149)
             Predict: 0.0
            Else (feature 3 > 5.04993896073149)
             If (feature 0 <= 5.987275954545455)
              Predict: 4.0
             Else (feature 0 > 5.987275954545455)
              Predict: 0.0
        Else (feature 2 > -1.21523575)
         If (feature 5 <= 1.9019736832530727)
          If (feature 4 <= 5.395001662922967)
           If (feature 4 <= 3.987483559659423)
            If (feature 0 <= -1.488667)
             If (feature 2 <= 0.6160089999999999)
              If (feature 0 <= -6.216001363636364)
               Predict: 0.0
              Else (feature 0 > -6.216001363636364)
               Predict: 2.0
             Else (feature 2 > 0.6160089999999999)
              Predict: 2.0
            Else (feature 0 > -1.488667)
             Predict: 0.0
           Else (feature 4 > 3.987483559659423)
            If (feature 0 <= 3.5434871363636367)
             Predict: 0.0
            Else (feature 0 > 3.5434871363636367)
             Predict: 4.0
          Else (feature 4 > 5.395001662922967)
           If (feature 5 <= 1.2763838461753882)
            Predict: 0.0
           Else (feature 5 > 1.2763838461753882)
            Predict: 4.0
         Else (feature 5 > 1.9019736832530727)
          If (feature 3 <= 5.89679045291164)
           If (feature 1 <= -10.122931363636361)
            Predict: 0.0
           Else (feature 1 > -10.122931363636361)
            If (feature 1 <= -6.371024409090909)
             If (feature 0 <= -1.488667)
              If (feature 4 <= 3.987483559659423)
               Predict: 2.0
              Else (feature 4 > 3.987483559659423)
               If (feature 2 <= 1.6994305454545455)
                If (feature 2 <= -0.5214064090909091)
                 If (feature 5 <= 3.104356065106381)
                  Predict: 0.0
                 Else (feature 5 > 3.104356065106381)
                  Predict: 2.0
                Else (feature 2 > -0.5214064090909091)
                 Predict: 0.0
               Else (feature 2 > 1.6994305454545455)
                Predict: 2.0
             Else (feature 0 > -1.488667)
              Predict: 2.0
            Else (feature 1 > -6.371024409090909)
             If (feature 4 <= 5.395001662922967)
              If (feature 0 <= -4.420172227272728)
               If (feature 1 <= -0.16313340909090912)
                If (feature 5 <= 3.803765702041731)
                 Predict: 0.0
                Else (feature 5 > 3.803765702041731)
                 If (feature 0 <= -6.216001363636364)
                  Predict: 2.0
                 Else (feature 0 > -6.216001363636364)
                  Predict: 0.0
               Else (feature 1 > -0.16313340909090912)
                If (feature 0 <= -5.033296227272727)
                 Predict: 0.0
                Else (feature 0 > -5.033296227272727)
                 Predict: 2.0
              Else (feature 0 > -4.420172227272728)
               Predict: 0.0
             Else (feature 4 > 5.395001662922967)
              If (feature 0 <= -2.5738281818181816)
               If (feature 0 <= -3.7931120454545457)
                Predict: 0.0
               Else (feature 0 > -3.7931120454545457)
                Predict: 2.0
              Else (feature 0 > -2.5738281818181816)
               If (feature 2 <= -1.0073793636363635)
                Predict: 4.0
               Else (feature 2 > -1.0073793636363635)
                Predict: 0.0
          Else (feature 3 > 5.89679045291164)
           Predict: 0.0
      Else (feature 4 > 5.856212462090488)
       If (feature 5 <= 2.815074767092767)
        If (feature 4 <= 7.749673922326561)
         If (feature 3 <= 8.669590934585441)
          If (feature 1 <= -9.359573909090908)
           If (feature 5 <= 1.468512909467716)
            If (feature 2 <= -0.6868815000000001)
             If (feature 0 <= -2.5738281818181816)
              Predict: 4.0
             Else (feature 0 > -2.5738281818181816)
              Predict: 2.0
            Else (feature 2 > -0.6868815000000001)
             If (feature 4 <= 7.040265431372278)
              Predict: 0.0
             Else (feature 4 > 7.040265431372278)
              Predict: 4.0
           Else (feature 5 > 1.468512909467716)
            If (feature 2 <= -5.8148077727272725)
             Predict: 2.0
            Else (feature 2 > -5.8148077727272725)
             If (feature 3 <= 2.06138891346951)
              If (feature 4 <= 6.293679874885813)
               If (feature 3 <= 1.3680974461096451)
                Predict: 0.0
               Else (feature 3 > 1.3680974461096451)
                Predict: 4.0
              Else (feature 4 > 6.293679874885813)
               Predict: 0.0
             Else (feature 3 > 2.06138891346951)
              Predict: 0.0
          Else (feature 1 > -9.359573909090908)
           If (feature 1 <= -1.2012645454545452)
            If (feature 0 <= -5.7328163636363625)
             If (feature 4 <= 6.293679874885813)
              If (feature 2 <= -1.4916079545454544)
               Predict: 0.0
              Else (feature 2 > -1.4916079545454544)
               If (feature 0 <= -6.216001363636364)
                Predict: 0.0
               Else (feature 0 > -6.216001363636364)
                Predict: 4.0
             Else (feature 4 > 6.293679874885813)
              If (feature 2 <= -1.7981704545454544)
               Predict: 0.0
              Else (feature 2 > -1.7981704545454544)
               Predict: 4.0
            Else (feature 0 > -5.7328163636363625)
             If (feature 2 <= -5.8148077727272725)
              Predict: 0.0
             Else (feature 2 > -5.8148077727272725)
              If (feature 1 <= -7.811519545454546)
               If (feature 0 <= -3.7931120454545457)
                If (feature 3 <= 3.2533446617122705)
                 Predict: 0.0
                Else (feature 3 > 3.2533446617122705)
                 Predict: 4.0
               Else (feature 0 > -3.7931120454545457)
                If (feature 2 <= 1.6994305454545455)
                 If (feature 0 <= 3.5434871363636367)
                  If (feature 5 <= 0.80494691075511)
                   Predict: 0.0
                  Else (feature 5 > 0.80494691075511)
                   If (feature 3 <= 3.2533446617122705)
                    If (feature 2 <= -1.7981704545454544)
                     Predict: 4.0
                    Else (feature 2 > -1.7981704545454544)
                     If (feature 5 <= 2.178632830786455)
                      If (feature 0 <= 2.0507363636363634)
                       Predict: 0.0
                      Else (feature 0 > 2.0507363636363634)
                       Predict: 4.0
                     Else (feature 5 > 2.178632830786455)
                      Predict: 0.0
                   Else (feature 3 > 3.2533446617122705)
                    Predict: 0.0
                 Else (feature 0 > 3.5434871363636367)
                  Predict: 0.0
                Else (feature 2 > 1.6994305454545455)
                 Predict: 2.0

*** WARNING: skipped 319338 bytes of output ***

         Predict: 0.0
     Else (feature 4 > 2.258741828976616)
      If (feature 5 <= 2.5963437348657123)
       If (feature 0 <= -3.125991409090909)
        If (feature 3 <= 4.165661639629755)
         If (feature 4 <= 2.884105112415355)
          If (feature 3 <= 2.713415564122834)
           If (feature 5 <= 1.6145607532142021)
            If (feature 0 <= -8.90539)
             Predict: 0.0
            Else (feature 0 > -8.90539)
             Predict: 2.0
           Else (feature 5 > 1.6145607532142021)
            Predict: 2.0
          Else (feature 3 > 2.713415564122834)
           Predict: 0.0
         Else (feature 4 > 2.884105112415355)
          If (feature 3 <= 1.3680974461096451)
           If (feature 1 <= -2.4344832727272725)
            If (feature 5 <= 1.9019736832530727)
             Predict: 4.0
            Else (feature 5 > 1.9019736832530727)
             Predict: 2.0
           Else (feature 1 > -2.4344832727272725)
            Predict: 0.0
          Else (feature 3 > 1.3680974461096451)
           If (feature 2 <= 1.6994305454545455)
            If (feature 2 <= 0.1979699090909091)
             Predict: 0.0
            Else (feature 2 > 0.1979699090909091)
             If (feature 3 <= 3.6472443306163704)
              Predict: 0.0
             Else (feature 3 > 3.6472443306163704)
              Predict: 4.0
           Else (feature 2 > 1.6994305454545455)
            Predict: 2.0
        Else (feature 3 > 4.165661639629755)
         If (feature 4 <= 5.856212462090488)
          If (feature 4 <= 3.987483559659423)
           If (feature 1 <= -9.513290454545455)
            If (feature 5 <= 1.2763838461753882)
             Predict: 0.0
            Else (feature 5 > 1.2763838461753882)
             If (feature 3 <= 4.655894911349467)
              Predict: 0.0
             Else (feature 3 > 4.655894911349467)
              Predict: 2.0
           Else (feature 1 > -9.513290454545455)
            Predict: 0.0
          Else (feature 4 > 3.987483559659423)
           Predict: 0.0
         Else (feature 4 > 5.856212462090488)
          If (feature 2 <= -1.21523575)
           Predict: 0.0
          Else (feature 2 > -1.21523575)
           Predict: 4.0
       Else (feature 0 > -3.125991409090909)
        If (feature 2 <= 1.0950141818181818)
         If (feature 0 <= 2.0507363636363634)
          If (feature 2 <= -1.7981704545454544)
           If (feature 2 <= -5.8148077727272725)
            If (feature 4 <= 6.684353189725881)
             If (feature 0 <= -1.488667)
              If (feature 1 <= -9.513290454545455)
               Predict: 2.0
              Else (feature 1 > -9.513290454545455)
               Predict: 0.0
             Else (feature 0 > -1.488667)
              Predict: 2.0
            Else (feature 4 > 6.684353189725881)
             Predict: 0.0
           Else (feature 2 > -5.8148077727272725)
            If (feature 1 <= -4.157154727272728)
             If (feature 4 <= 3.509467511028114)
              If (feature 0 <= -2.5738281818181816)
               Predict: 2.0
              Else (feature 0 > -2.5738281818181816)
               If (feature 5 <= 2.374697522458404)
                Predict: 0.0
               Else (feature 5 > 2.374697522458404)
                Predict: 2.0
             Else (feature 4 > 3.509467511028114)
              If (feature 0 <= -0.3738945909090909)
               If (feature 3 <= 1.8104608428061633)
                Predict: 4.0
               Else (feature 3 > 1.8104608428061633)
                If (feature 4 <= 5.395001662922967)
                 Predict: 0.0
                Else (feature 4 > 5.395001662922967)
                 Predict: 4.0
              Else (feature 0 > -0.3738945909090909)
               If (feature 4 <= 5.856212462090488)
                Predict: 2.0
               Else (feature 4 > 5.856212462090488)
                Predict: 4.0
            Else (feature 1 > -4.157154727272728)
             Predict: 0.0
          Else (feature 2 > -1.7981704545454544)
           If (feature 1 <= -7.811519545454546)
            If (feature 3 <= 1.1186607583073207)
             Predict: 1.0
            Else (feature 3 > 1.1186607583073207)
             Predict: 2.0
           Else (feature 1 > -7.811519545454546)
            If (feature 1 <= -5.200512090909092)
             If (feature 3 <= 2.06138891346951)
              Predict: 4.0
             Else (feature 3 > 2.06138891346951)
              If (feature 2 <= 0.6160089999999999)
               If (feature 0 <= 0.9951855113636363)
                Predict: 0.0
               Else (feature 0 > 0.9951855113636363)
                If (feature 5 <= 1.076775279931446)
                 Predict: 0.0
                Else (feature 5 > 1.076775279931446)
                 Predict: 4.0
              Else (feature 2 > 0.6160089999999999)
               If (feature 0 <= -1.488667)
                Predict: 2.0
               Else (feature 0 > -1.488667)
                Predict: 4.0
            Else (feature 1 > -5.200512090909092)
             If (feature 5 <= 1.076775279931446)
              If (feature 3 <= 2.29340842981981)
               Predict: 2.0
              Else (feature 3 > 2.29340842981981)
               Predict: 4.0
             Else (feature 5 > 1.076775279931446)
              If (feature 0 <= 1.2947807727272727)
               Predict: 0.0
              Else (feature 0 > 1.2947807727272727)
               If (feature 3 <= 1.6040286540977868)
                Predict: 4.0
               Else (feature 3 > 1.6040286540977868)
                Predict: 0.0
         Else (feature 0 > 2.0507363636363634)
          If (feature 4 <= 5.01193131655486)
           If (feature 1 <= -13.949734999999999)
            Predict: 0.0
           Else (feature 1 > -13.949734999999999)
            If (feature 3 <= 3.2533446617122705)
             If (feature 1 <= -7.391737681818182)
              Predict: 2.0
             Else (feature 1 > -7.391737681818182)
              Predict: 0.0
            Else (feature 3 > 3.2533446617122705)
             Predict: 0.0
          Else (feature 4 > 5.01193131655486)
           If (feature 1 <= -8.71901181818182)
            If (feature 2 <= -5.8148077727272725)
             Predict: 2.0
            Else (feature 2 > -5.8148077727272725)
             Predict: 0.0
           Else (feature 1 > -8.71901181818182)
            If (feature 3 <= 8.669590934585441)
             If (feature 1 <= -1.2012645454545452)
              If (feature 3 <= 1.6040286540977868)
               Predict: 0.0
              Else (feature 3 > 1.6040286540977868)
               If (feature 4 <= 9.024711300064961)
                If (feature 4 <= 8.135808679557085)
                 If (feature 1 <= -8.649340000000002)
                  If (feature 0 <= 2.8798476363636363)
                   Predict: 4.0
                  Else (feature 0 > 2.8798476363636363)
                   Predict: 0.0
                 Else (feature 1 > -8.649340000000002)
                  If (feature 5 <= 2.178632830786455)
                   If (feature 0 <= 5.987275954545455)
                    If (feature 4 <= 7.040265431372278)
                     If (feature 1 <= -6.371024409090909)
                      If (feature 5 <= 1.076775279931446)
                       Predict: 4.0
                      Else (feature 5 > 1.076775279931446)
                       Predict: 0.0
                     Else (feature 1 > -6.371024409090909)
                      Predict: 4.0
                    Else (feature 4 > 7.040265431372278)
                     Predict: 4.0
                   Else (feature 0 > 5.987275954545455)
                    If (feature 4 <= 6.293679874885813)
                     If (feature 5 <= 1.9019736832530727)
                      Predict: 4.0
                     Else (feature 5 > 1.9019736832530727)
                      Predict: 0.0
                    Else (feature 4 > 6.293679874885813)
                     Predict: 4.0
                  Else (feature 5 > 2.178632830786455)
                   If (feature 2 <= -0.6868815000000001)
                    If (feature 3 <= 2.713415564122834)
                     Predict: 0.0
                    Else (feature 3 > 2.713415564122834)
                     If (feature 4 <= 6.293679874885813)
                      If (feature 0 <= 5.987275954545455)
                       Predict: 4.0
                      Else (feature 0 > 5.987275954545455)
                       If (feature 4 <= 5.395001662922967)
                        Predict: 4.0
                       Else (feature 4 > 5.395001662922967)
                        Predict: 0.0
                     Else (feature 4 > 6.293679874885813)
                      Predict: 4.0
                   Else (feature 2 > -0.6868815000000001)
                    If (feature 0 <= 3.5434871363636367)
                     Predict: 4.0
                    Else (feature 0 > 3.5434871363636367)
                     Predict: 0.0
                Else (feature 4 > 8.135808679557085)
                 If (feature 3 <= 2.29340842981981)
                  Predict: 0.0
                 Else (feature 3 > 2.29340842981981)
                  If (feature 3 <= 4.165661639629755)
                   Predict: 4.0
                  Else (feature 3 > 4.165661639629755)
                   If (feature 3 <= 6.530604828890175)
                    Predict: 0.0
                   Else (feature 3 > 6.530604828890175)
                    Predict: 4.0
               Else (feature 4 > 9.024711300064961)
                Predict: 0.0
             Else (feature 1 > -1.2012645454545452)
              Predict: 0.0
            Else (feature 3 > 8.669590934585441)
             Predict: 0.0
        Else (feature 2 > 1.0950141818181818)
         If (feature 2 <= 1.6994305454545455)
          If (feature 1 <= -5.200512090909092)
           If (feature 4 <= 5.01193131655486)
            Predict: 2.0
           Else (feature 4 > 5.01193131655486)
            If (feature 0 <= 2.8798476363636363)
             If (feature 3 <= 2.952235990607485)
              Predict: 4.0
             Else (feature 3 > 2.952235990607485)
              If (feature 4 <= 5.856212462090488)
               Predict: 2.0
              Else (feature 4 > 5.856212462090488)
               Predict: 0.0
            Else (feature 0 > 2.8798476363636363)
             Predict: 0.0
          Else (feature 1 > -5.200512090909092)
           Predict: 0.0
         Else (feature 2 > 1.6994305454545455)
          If (feature 0 <= -2.0286351363636363)
           If (feature 5 <= 2.178632830786455)
            Predict: 2.0
           Else (feature 5 > 2.178632830786455)
            Predict: 0.0
          Else (feature 0 > -2.0286351363636363)
           If (feature 4 <= 8.135808679557085)
            Predict: 0.0
           Else (feature 4 > 8.135808679557085)
            If (feature 3 <= 2.952235990607485)
             If (feature 0 <= -0.16835886363636363)
              Predict: 0.0
             Else (feature 0 > -0.16835886363636363)
              Predict: 4.0
            Else (feature 3 > 2.952235990607485)
             Predict: 0.0
      Else (feature 5 > 2.5963437348657123)
       If (feature 4 <= 4.517274572453781)
        If (feature 3 <= 3.2533446617122705)
         If (feature 1 <= -4.157154727272728)
          If (feature 0 <= -8.90539)
           Predict: 0.0
          Else (feature 0 > -8.90539)
           If (feature 1 <= -17.560554999999994)
            Predict: 0.0
           Else (feature 1 > -17.560554999999994)
            If (feature 3 <= 1.1186607583073207)
             Predict: 4.0
            Else (feature 3 > 1.1186607583073207)
             If (feature 1 <= -6.928410727272727)
              Predict: 2.0
             Else (feature 1 > -6.928410727272727)
              If (feature 4 <= 3.509467511028114)
               Predict: 2.0
              Else (feature 4 > 3.509467511028114)
               Predict: 0.0
         Else (feature 1 > -4.157154727272728)
          If (feature 2 <= 1.0950141818181818)
           Predict: 0.0
          Else (feature 2 > 1.0950141818181818)
           Predict: 2.0
        Else (feature 3 > 3.2533446617122705)
         If (feature 0 <= -0.7518725909090909)
          If (feature 3 <= 3.6472443306163704)
           If (feature 2 <= 0.1979699090909091)
            If (feature 0 <= -2.5738281818181816)
             Predict: 0.0
            Else (feature 0 > -2.5738281818181816)
             Predict: 2.0
           Else (feature 2 > 0.1979699090909091)
            Predict: 2.0
          Else (feature 3 > 3.6472443306163704)
           If (feature 5 <= 2.815074767092767)
            If (feature 2 <= 0.1979699090909091)
             Predict: 0.0
            Else (feature 2 > 0.1979699090909091)
             If (feature 4 <= 3.987483559659423)
              Predict: 2.0
             Else (feature 4 > 3.987483559659423)
              Predict: 0.0
           Else (feature 5 > 2.815074767092767)
            If (feature 3 <= 4.655894911349467)
             If (feature 4 <= 3.987483559659423)
              Predict: 0.0
             Else (feature 4 > 3.987483559659423)
              If (feature 1 <= -7.811519545454546)
               If (feature 2 <= -1.4916079545454544)
                Predict: 2.0
               Else (feature 2 > -1.4916079545454544)
                Predict: 0.0
              Else (feature 1 > -7.811519545454546)
               Predict: 0.0
            Else (feature 3 > 4.655894911349467)
             Predict: 0.0
         Else (feature 0 > -0.7518725909090909)
          Predict: 0.0
       Else (feature 4 > 4.517274572453781)
        If (feature 3 <= 4.165661639629755)
         If (feature 0 <= 2.0507363636363634)
          If (feature 5 <= 5.9923123904255196)
           If (feature 2 <= -1.7981704545454544)
            If (feature 1 <= -4.157154727272728)
             If (feature 1 <= -7.391737681818182)
              If (feature 4 <= 7.040265431372278)
               If (feature 2 <= -5.8148077727272725)
                If (feature 3 <= 2.29340842981981)
                 Predict: 2.0
                Else (feature 3 > 2.29340842981981)
                 Predict: 0.0
               Else (feature 2 > -5.8148077727272725)
                If (feature 5 <= 3.465871724305953)
                 If (feature 0 <= -2.5738281818181816)
                  Predict: 4.0
                 Else (feature 0 > -2.5738281818181816)
                  Predict: 2.0
                Else (feature 5 > 3.465871724305953)
                 Predict: 2.0
              Else (feature 4 > 7.040265431372278)
               If (feature 5 <= 2.815074767092767)
                Predict: 4.0
               Else (feature 5 > 2.815074767092767)
                Predict: 0.0
             Else (feature 1 > -7.391737681818182)
              If (feature 3 <= 1.6040286540977868)
               Predict: 0.0
              Else (feature 3 > 1.6040286540977868)
               If (feature 0 <= -3.125991409090909)
                Predict: 0.0
               Else (feature 0 > -3.125991409090909)
                Predict: 4.0
            Else (feature 1 > -4.157154727272728)
             Predict: 0.0
           Else (feature 2 > -1.7981704545454544)
            If (feature 1 <= -4.157154727272728)
             If (feature 5 <= 3.803765702041731)
              If (feature 5 <= 3.465871724305953)
               If (feature 1 <= -5.8293135909090905)
                If (feature 4 <= 6.293679874885813)
                 If (feature 0 <= -3.125991409090909)
                  Predict: 0.0
                 Else (feature 0 > -3.125991409090909)
                  If (feature 2 <= 0.6160089999999999)
                   Predict: 2.0
                  Else (feature 2 > 0.6160089999999999)
                   Predict: 0.0
                Else (feature 4 > 6.293679874885813)
                 If (feature 5 <= 2.815074767092767)
                  Predict: 0.0
                 Else (feature 5 > 2.815074767092767)
                  Predict: 2.0
               Else (feature 1 > -5.8293135909090905)
                If (feature 2 <= -1.073567681818182)
                 Predict: 4.0
                Else (feature 2 > -1.073567681818182)
                 If (feature 4 <= 5.01193131655486)
                  Predict: 0.0
                 Else (feature 4 > 5.01193131655486)
                  If (feature 4 <= 6.684353189725881)
                   Predict: 2.0
                  Else (feature 4 > 6.684353189725881)
                   Predict: 0.0
              Else (feature 5 > 3.465871724305953)
               Predict: 2.0
             Else (feature 5 > 3.803765702041731)
              If (feature 3 <= 2.499281243538517)
               If (feature 4 <= 7.374296497627369)
                Predict: 2.0
               Else (feature 4 > 7.374296497627369)
                If (feature 4 <= 8.135808679557085)
                 Predict: 0.0
                Else (feature 4 > 8.135808679557085)
                 Predict: 4.0
              Else (feature 3 > 2.499281243538517)
               Predict: 0.0
            Else (feature 1 > -4.157154727272728)
             If (feature 1 <= -2.4344832727272725)
              If (feature 4 <= 7.040265431372278)
               Predict: 0.0
              Else (feature 4 > 7.040265431372278)
               Predict: 4.0
             Else (feature 1 > -2.4344832727272725)
              Predict: 0.0
          Else (feature 5 > 5.9923123904255196)
           If (feature 5 <= 8.512274217664926)
            If (feature 0 <= 0.32806340909090914)
             Predict: 0.0
            Else (feature 0 > 0.32806340909090914)
             If (feature 1 <= -5.200512090909092)
              If (feature 2 <= -3.574838818181818)
               Predict: 4.0
              Else (feature 2 > -3.574838818181818)
               Predict: 0.0
             Else (feature 1 > -5.200512090909092)
              Predict: 0.0
           Else (feature 5 > 8.512274217664926)
            Predict: 0.0
         Else (feature 0 > 2.0507363636363634)
          If (feature 2 <= -5.8148077727272725)
           If (feature 3 <= 1.6040286540977868)
            Predict: 2.0
           Else (feature 3 > 1.6040286540977868)
            Predict: 0.0
          Else (feature 2 > -5.8148077727272725)
           If (feature 3 <= 3.6472443306163704)
            Predict: 0.0
           Else (feature 3 > 3.6472443306163704)
            If (feature 1 <= -6.371024409090909)
             Predict: 0.0
            Else (feature 1 > -6.371024409090909)
             If (feature 1 <= -5.200512090909092)
              Predict: 4.0
             Else (feature 1 > -5.200512090909092)
              Predict: 0.0
        Else (feature 3 > 4.165661639629755)
         If (feature 5 <= 2.815074767092767)
          If (feature 0 <= -2.5738281818181816)
           Predict: 0.0
          Else (feature 0 > -2.5738281818181816)
           If (feature 2 <= -0.6868815000000001)
            If (feature 3 <= 8.669590934585441)
             If (feature 0 <= 7.339635468181818)
              If (feature 4 <= 7.749673922326561)
               If (feature 0 <= 5.987275954545455)
                Predict: 4.0
               Else (feature 0 > 5.987275954545455)
                If (feature 3 <= 7.301299272895662)
                 Predict: 4.0
                Else (feature 3 > 7.301299272895662)
                 Predict: 0.0
              Else (feature 4 > 7.749673922326561)
               Predict: 0.0
             Else (feature 0 > 7.339635468181818)
              Predict: 0.0
            Else (feature 3 > 8.669590934585441)
             Predict: 0.0
           Else (feature 2 > -0.6868815000000001)
            If (feature 4 <= 7.749673922326561)
             Predict: 0.0
            Else (feature 4 > 7.749673922326561)
             If (feature 3 <= 5.45309454568844)
              Predict: 4.0
             Else (feature 3 > 5.45309454568844)
              Predict: 0.0
         Else (feature 5 > 2.815074767092767)
          If (feature 3 <= 5.45309454568844)
           If (feature 1 <= -7.811519545454546)
            If (feature 0 <= -4.420172227272728)
             If (feature 5 <= 3.465871724305953)
              If (feature 0 <= -7.16007390909091)
               Predict: 0.0
              Else (feature 0 > -7.16007390909091)
               Predict: 2.0
             Else (feature 5 > 3.465871724305953)
              Predict: 0.0
            Else (feature 0 > -4.420172227272728)
             If (feature 4 <= 7.749673922326561)
              If (feature 5 <= 4.209746983589046)
               If (feature 3 <= 5.04993896073149)
                Predict: 0.0
               Else (feature 3 > 5.04993896073149)
                If (feature 2 <= -0.5214064090909091)
                 Predict: 2.0
                Else (feature 2 > -0.5214064090909091)
                 Predict: 0.0
              Else (feature 5 > 4.209746983589046)
               Predict: 0.0
             Else (feature 4 > 7.749673922326561)
              If (feature 2 <= -2.8084323636363635)
               If (feature 1 <= -9.513290454545455)
                Predict: 0.0
               Else (feature 1 > -9.513290454545455)
                If (feature 0 <= 2.8798476363636363)
                 Predict: 4.0
                Else (feature 0 > 2.8798476363636363)
                 Predict: 0.0
              Else (feature 2 > -2.8084323636363635)
               If (feature 1 <= -11.699289545454546)
                If (feature 5 <= 4.209746983589046)
                 If (feature 0 <= -2.0286351363636363)
                  Predict: 0.0
                 Else (feature 0 > -2.0286351363636363)
                  Predict: 2.0
                Else (feature 5 > 4.209746983589046)
                 Predict: 0.0
               Else (feature 1 > -11.699289545454546)
                Predict: 0.0
           Else (feature 1 > -7.811519545454546)
            If (feature 0 <= 2.8798476363636363)
             If (feature 4 <= 7.040265431372278)
              If (feature 3 <= 5.04993896073149)
               If (feature 0 <= -1.488667)
                Predict: 0.0
               Else (feature 0 > -1.488667)
                If (feature 0 <= -0.7518725909090909)
                 Predict: 2.0
                Else (feature 0 > -0.7518725909090909)
                 Predict: 0.0
              Else (feature 3 > 5.04993896073149)
               If (feature 5 <= 3.803765702041731)
                Predict: 0.0
               Else (feature 5 > 3.803765702041731)
                Predict: 2.0
             Else (feature 4 > 7.040265431372278)
              If (feature 4 <= 9.024711300064961)
               If (feature 4 <= 7.374296497627369)
                If (feature 0 <= 0.9951855113636363)
                 Predict: 4.0
                Else (feature 0 > 0.9951855113636363)
                 Predict: 0.0
               Else (feature 4 > 7.374296497627369)
                If (feature 2 <= -5.8148077727272725)
                 Predict: 0.0
                Else (feature 2 > -5.8148077727272725)
                 Predict: 4.0
              Else (feature 4 > 9.024711300064961)
               Predict: 0.0
            Else (feature 0 > 2.8798476363636363)
             Predict: 0.0
          Else (feature 3 > 5.45309454568844)
           If (feature 1 <= -5.8293135909090905)
            If (feature 4 <= 8.135808679557085)
             Predict: 0.0
            Else (feature 4 > 8.135808679557085)
             If (feature 3 <= 5.89679045291164)
              If (feature 5 <= 4.852637451173388)
               If (feature 5 <= 3.465871724305953)
                Predict: 0.0
               Else (feature 5 > 3.465871724305953)
                Predict: 4.0
              Else (feature 5 > 4.852637451173388)
               Predict: 0.0
             Else (feature 3 > 5.89679045291164)
              Predict: 0.0
           Else (feature 1 > -5.8293135909090905)
            If (feature 3 <= 7.301299272895662)
             If (feature 0 <= 0.9951855113636363)
              Predict: 0.0
             Else (feature 0 > 0.9951855113636363)
              If (feature 4 <= 5.856212462090488)
               Predict: 0.0
              Else (feature 4 > 5.856212462090488)
               If (feature 0 <= 5.987275954545455)
                If (feature 5 <= 3.465871724305953)
                 Predict: 4.0
                Else (feature 5 > 3.465871724305953)
                 Predict: 0.0
               Else (feature 0 > 5.987275954545455)
                Predict: 0.0
            Else (feature 3 > 7.301299272895662)
             If (feature 1 <= -5.200512090909092)
              If (feature 4 <= 7.374296497627369)
               Predict: 0.0
              Else (feature 4 > 7.374296497627369)
               If (feature 5 <= 3.104356065106381)
                Predict: 4.0
               Else (feature 5 > 3.104356065106381)
                Predict: 0.0
             Else (feature 1 > -5.200512090909092)
              Predict: 0.0

import org.apache.spark.ml.classification.RandomForestClassificationModel
rfModel: org.apache.spark.ml.classification.RandomForestClassificationModel = RandomForestClassificationModel: uid=rfc_794232dabcdf, numTrees=10, numClasses=5, numFeatures=6

Save and Load later to Serve Predictions

When you are satisfied with the model you have trained/fitted then you can save it to a file and load it again from another low-latency prediciton-serving system to serve predictions.

model
res27: org.apache.spark.ml.PipelineModel = pipeline_76d41a70ccc7
import org.apache.spark.ml.PipelineModel
import org.apache.spark.ml.PipelineModel

Save the model to a file in stable storage.

model.write.overwrite().save("/datasets/sds/ActivityRecognition/preTrainedModels/myRandomForestClassificationModelAsPipeLineModel")

Load the model, typically from a prediction or model serving layer/system.

val same_rfModelFromSavedFile = PipelineModel.load("/datasets/sds/ActivityRecognition/preTrainedModels/myRandomForestClassificationModelAsPipeLineModel")
same_rfModelFromSavedFile: org.apache.spark.ml.PipelineModel = pipeline_76d41a70ccc7
same_rfModelFromSavedFile
res29: org.apache.spark.ml.PipelineModel = pipeline_76d41a70ccc7

Suppose new data is coming at us and we need to serve our predicitons of the activities

Note: We only need accelerometer readings so prediciton pipeline can be simplified to only take in the needed features for prediction. For simplicity let's assume the test data is representative of the new data (previously unseen) that is coming at us for serving our activity predicitons.

val newDataForPrediction = testData.sample(0.0004,12348L) // get a random test data as new data for prediction
display(newDataForPrediction.select("meanX", "meanY", "meanZ", "stddevX", "stddevY","stddevZ")) // showing only features that will be used by model for prediction
meanX meanY meanZ stddevX stddevY stddevZ
-2.504156 -9.297302727272728 -1.3522605454545453 2.1172874206915644 1.2430011314330338 2.6961258744053342

Here is another new data coming at you... you can predict the current activity being done by simply transforming the loaded model (estimator).

val newDataForPrediction = testData.sample(0.0004,1234L) // get a random test data as new data for prediction
display(newDataForPrediction.select("meanX", "meanY", "meanZ", "stddevX", "stddevY","stddevZ")) // showing only features that will be used by model for prediction
meanX meanY meanZ stddevX stddevY stddevZ
0.4465079090909091 -0.6821994545454545 9.447101818181817 8.440257552550214e-2 0.10589937675019803 6.67451371767209e-2
display(same_rfModelFromSavedFile.transform(newDataForPrediction).select("meanX", "meanY", "meanZ", "stddevX", "stddevY","stddevZ","prediction"))
meanX meanY meanZ stddevX stddevY stddevZ prediction
0.4465079090909091 -0.6821994545454545 9.447101818181817 8.440257552550214e-2 0.10589937675019803 6.67451371767209e-2 3.0

Some minor post-processing to connect prediction label to the activity string.

Typically one prediction is just a small part of larger business or science use-case.

activityLabelDF.show
+--------+-----+
|activity|label|
+--------+-----+
| Jogging|  0.0|
| Jumping|  4.0|
|Standing|  1.0|
| Walking|  2.0|
| Sitting|  3.0|
+--------+-----+
display(same_rfModelFromSavedFile
        .transform(newDataForPrediction)
        .select("meanX", "meanY", "meanZ", "stddevX", "stddevY","stddevZ","prediction")
        .join(activityLabelDF,$"prediction"===$"label")
        .drop("prediction","label")
        .withColumnRenamed("activity","Your current activity is likely to be")
       )
meanX meanY meanZ stddevX stddevY stddevZ Your current activity is likely to be
0.4465079090909091 -0.6821994545454545 9.447101818181817 8.440257552550214e-2 0.10589937675019803 6.67451371767209e-2 Sitting

An activity-based music-recommendation system - a diatribe:

For example, you may want to correlate historical music-listening habits for a user with their historical physical activities and then recommend music to them using a subsequent recommender system pipeline that uses activity prediciton as one of its input.

NOTE: One has to be legally compliant for using the data in such manner with client consent, depending on the jurisdiction of your operations - GDPR applies for EU operations, for example --- this is coming attraction!

display(same_rfModelFromSavedFile.transform(testData.sample(0.01))) // note more can be done with such data, time of day can be informative for other decision problems
  1. Download and Load Data

The following anonymized dataset is used with kind permission of Amira Lakhal.

wget http://lamastex.org/datasets/public/ActivityRecognition/dataTraining.csv
pwd && ls
//dbutils.fs.mkdirs("dbfs:///datasets/sds/ActivityRecognition") // make directory if needed
dbutils.fs.mv("file:///databricks/driver/dataTraining.csv","/datasets/sds/ActivityRecognition/dataTraining.csv")
res38: Boolean = true
display(dbutils.fs.ls("/datasets/sds/ActivityRecognition"))
path name size
dbfs:/datasets/sds/ActivityRecognition/dataTraining.csv dataTraining.csv 931349.0
dbfs:/datasets/sds/ActivityRecognition/preTrainedModels/ preTrainedModels/ 0.0
dbutils.fs.head("/datasets/sds/ActivityRecognition/dataTraining.csv")
[Truncated to first 65536 bytes]
res40: String =
"user_id","activity","timeStampAsLong","x","y","z"
"user_001","Jumping",1446047227606,"4.33079","-12.72175","-3.18118"
"user_001","Jumping",1446047227671,"0.575403","-0.727487","2.95007"
"user_001","Jumping",1446047227735,"-1.60885","3.52607","-0.1922"
"user_001","Jumping",1446047227799,"0.690364","-0.037722","1.72382"
"user_001","Jumping",1446047227865,"3.44943","-1.68549","2.29862"
"user_001","Jumping",1446047227930,"1.87829","-1.91542","0.880768"
"user_001","Jumping",1446047227995,"1.57173","-5.86241","-3.75599"
"user_001","Jumping",1446047228059,"3.41111","-17.93331","0.535886"
"user_001","Jumping",1446047228123,"3.18118","-19.58108","5.74745"
"user_001","Jumping",1446047228189,"7.85626","-19.2362","0.804128"
"user_001","Jumping",1446047228253,"1.26517","-8.85139","2.18366"
"user_001","Jumping",1446047228318,"0.077239","1.15021","1.53221"
"user_001","Jumping",1446047228383,"0.230521","2.0699","-1.41845"
"user_001","Jumping",1446047228447,"0.652044","-0.497565","1.76214"
"user_001","Jumping",1446047228512,"1.53341","-0.305964","1.41725"
"user_001","Jumping",1446047228578,"-1.07237","-1.95374","0.191003"
"user_001","Jumping",1446047228642,"2.75966","-13.75639","0.191003"
"user_001","Jumping",1446047228707,"7.43474","-19.58108","2.95007"
"user_001","Jumping",1446047228771,"5.63368","-19.58108","5.59417"
"user_001","Jumping",1446047228836,"5.02056","-11.72542","-1.38013"
"user_001","Jumping",1446047228900,"-2.10702","0.575403","1.07237"
"user_001","Jumping",1446047228966,"-1.30229","2.2615","-1.26517"
"user_001","Jumping",1446047229030,"1.68669","-0.957409","1.57053"
"user_001","Jumping",1446047229095,"2.60638","-0.229323","2.14534"
"user_001","Jumping",1446047229159,"1.30349","-0.152682","0.497565"
"user_001","Jumping",1446047229224,"1.64837","-8.12331","1.60885"
"user_001","Jumping",1446047229290,"0.15388","-18.46979","-1.03525"
"user_001","Jumping",1446047229354,"4.98224","-19.58108","0.995729"
"user_001","Jumping",1446047229419,"5.17384","-19.2362","0.612526"
"user_001","Jumping",1446047229483,"2.03158","-9.11964","1.34061"
"user_001","Jumping",1446047229549,"-1.95374","-1.03405","0.574206"
"user_001","Jumping",1446047229612,"0.1922","1.30349","-1.03525"
"user_001","Jumping",1446047229678,"1.64837","-0.727487","-0.307161"
"user_001","Jumping",1446047229743,"2.56806","-1.03405","0.267643"
"user_001","Jumping",1446047229806,"1.41845","-0.305964","0.727487"
"user_001","Jumping",1446047229872,"1.03525","-6.82042","0.957409"
"user_001","Jumping",1446047229936,"3.94759","-19.31284","-1.22685"
"user_001","Jumping",1446047230001,"6.13185","-19.58108","2.72014"
"user_001","Jumping",1446047230066,"7.89458","-16.9753","0.229323"
"user_001","Jumping",1446047230131,"2.6447","-3.75479","0.114362"
"user_001","Jumping",1446047230195,"-2.41358","1.91661","-0.000599"
"user_001","Jumping",1446047230260,"-1.95374","-0.114362","-0.268841"
"user_001","Jumping",1446047230325,"-0.229323","-1.95374","2.75846"
"user_001","Jumping",1446047230390,"2.68302","0.268841","0.535886"
"user_001","Jumping",1446047230455,"1.15021","-1.41725","0.880768"
"user_001","Jumping",1446047230519,"2.98958","-11.53382","-0.920286"
"user_001","Jumping",1446047230584,"8.00954","-19.58108","-0.1922"
"user_001","Jumping",1446047230649,"7.31978","-19.58108","2.52854"
"user_001","Jumping",1446047230713,"5.44208","-13.56479","-0.498763"
"user_001","Jumping",1446047230779,"0.728685","-0.420925","1.68549"
"user_001","Jumping",1446047230842,"1.18853","1.41845","-2.22318"
"user_001","Jumping",1446047230907,"0.15388","-1.80046","2.03038"
"user_001","Jumping",1446047230972,"-0.037722","1.07357","-0.958607"
"user_001","Jumping",1446047231038,"0.230521","0.728685","-0.690364"
"user_001","Jumping",1446047231102,"0.805325","-1.14901","1.53221"
"user_001","Jumping",1446047231167,"5.17384","-9.15796","-2.91294"
"user_001","Jumping",1446047231231,"8.00954","-19.54276","1.49389"
"user_001","Jumping",1446047231296,"11.61165","-19.58108","4.25296"
"user_001","Jumping",1446047231361,"7.89458","-18.35483","3.71647"
"user_001","Jumping",1446047231426,"0.537083","-3.21831","0.420925"
"user_001","Jumping",1446047231490,"-1.91542","4.10087","-2.6447"
"user_001","Jumping",1446047231555,"-0.919089","-0.382604","0.114362"
"user_001","Jumping",1446047231620,"0.613724","-0.842448","1.57053"
"user_001","Jumping",1446047231684,"1.38013","-0.459245","0.305964"
"user_001","Jumping",1446047231749,"2.29982","-1.49389","-1.26517"
"user_001","Jumping",1446047231814,"4.94392","-10.95901","-0.498763"
"user_001","Jumping",1446047231878,"3.75599","-19.27452","-1.76333"
"user_001","Jumping",1446047231944,"7.70298","-19.58108","-2.95126"
"user_001","Jumping",1446047232008,"6.55337","-17.51178","-1.91661"
"user_001","Jumping",1446047232073,"2.10822","-2.03038","-0.268841"
"user_001","Jumping",1446047232138,"-1.68549","3.67935","-0.881966"
"user_001","Jumping",1446047232203,"0.15388","-0.114362","0.076042"
"user_001","Jumping",1446047232267,"2.79798","-1.95374","0.689167"
"user_001","Jumping",1446047232332,"1.45677","-0.957409","0.420925"
"user_001","Jumping",1446047232397,"1.18853","-2.95007","0.650847"
"user_001","Jumping",1446047232462,"3.44943","-13.87135","-3.71767"
"user_001","Jumping",1446047232526,"3.79431","-19.58108","-0.345482"
"user_001","Jumping",1446047232591,"6.09353","-19.58108","2.87342"
"user_001","Jumping",1446047232655,"4.48408","-14.3312","-0.498763"
"user_001","Jumping",1446047232720,"-0.037722","-1.68549","2.6435"
"user_001","Jumping",1446047232785,"0.613724","2.68302","-2.37646"
"user_001","Jumping",1446047232850,"0.996927","-0.497565","0.497565"
"user_001","Jumping",1446047232915,"0.15388","-0.689167","1.34061"
"user_001","Jumping",1446047232979,"1.07357","1.07357","-2.60638"
"user_001","Jumping",1446047233044,"2.37646","-3.29495","-1.45677"
"user_001","Jumping",1446047233109,"2.22318","-16.09393","1.37893"
"user_001","Jumping",1446047233173,"6.82161","-19.58108","0.037722"
"user_001","Jumping",1446047233238,"8.39275","-19.54276","1.22565"
"user_001","Jumping",1446047233303,"1.22685","-9.50284","-0.307161"
"user_001","Jumping",1446047233368,"1.83997","-0.152682","1.41725"
"user_001","Jumping",1446047233432,"-0.765807","0.996927","-1.91661"
"user_001","Jumping",1446047233497,"0.728685","-0.612526","0.152682"
"user_001","Jumping",1446047233562,"0.996927","-0.305964","0.995729"
"user_001","Jumping",1446047233626,"1.22685","-0.305964","0.037722"
"user_001","Jumping",1446047233692,"1.91661","-2.95007","-0.345482"
"user_001","Jumping",1446047233755,"4.75232","-14.63776","-3.67935"
"user_001","Jumping",1446047233821,"4.56072","-19.58108","-2.6447"
"user_001","Jumping",1446047233886,"10.69197","-19.38948","-5.94025"
"user_001","Jumping",1446047233950,"3.10454","-10.42253","-2.22318"
"user_001","Jumping",1446047234015,"-0.152682","1.61005","1.80046"
"user_001","Jumping",1446047234080,"-0.267643","1.83997","-0.958607"
"user_001","Jumping",1446047234145,"1.99325","-0.842448","-0.230521"
"user_001","Jumping",1446047234210,"2.79798","-0.114362","0.919089"
"user_001","Jumping",1446047234273,"1.11189","-0.152682","1.83878"
"user_001","Jumping",1446047234339,"2.75966","-5.05768","-0.537083"
"user_001","Jumping",1446047234403,"4.33079","-16.82202","-3.06622"
"user_001","Jumping",1446047234468,"6.89825","-19.58108","-4.25415"
"user_001","Jumping",1446047234533,"11.49669","-19.50444","-2.52974"
"user_001","Jumping",1446047234598,"6.20849","-9.08132","-1.80165"
"user_001","Jumping",1446047234663,"0.805325","1.15021","-0.15388"
"user_001","Jumping",1446047234726,"-1.76214","2.14654","-0.460442"
"user_001","Jumping",1446047234792,"0.000599","-1.11069","-0.230521"
"user_001","Jumping",1446047234857,"0.652044","0.230521","-0.920286"
"user_001","Jumping",1446047234922,"1.26517","-0.114362","-0.000599"
"user_001","Jumping",1446047234986,"5.36544","-4.09967","-0.537083"
"user_001","Jumping",1446047235051,"6.51505","-17.05194","-3.56439"
"user_001","Jumping",1446047235115,"6.93658","-19.58108","-2.75966"
"user_001","Jumping",1446047235181,"7.89458","-19.58108","-3.18118"
"user_001","Jumping",1446047235245,"1.95493","-9.6178","-1.34181"
"user_001","Jumping",1446047235310,"-2.18366","3.14286","-0.1922"
"user_001","Jumping",1446047235375,"-2.87342","1.99325","-1.76333"
"user_001","Jumping",1446047235439,"1.03525","-1.80046","1.64717"
"user_001","Jumping",1446047235504,"1.95493","-0.689167","1.49389"
"user_001","Jumping",1446047235569,"1.26517","0.383802","-0.307161"
"user_001","Jumping",1446047235633,"1.18853","-2.72014","1.41725"
"user_001","Jumping",1446047235698,"5.71033","-16.51545","-2.03158"
"user_001","Jumping",1446047235763,"6.55337","-19.58108","0.995729"
"user_001","Jumping",1446047235828,"10.577","-19.4278","-1.57173"
"user_001","Jumping",1446047235892,"2.79798","-9.88604","-0.843646"
"user_001","Jumping",1446047235957,"0.652044","-0.037722","1.14901"
"user_001","Jumping",1446047236022,"0.843646","1.95493","-2.14654"
"user_001","Jumping",1446047236086,"0.15388","-0.305964","0.995729"
"user_001","Jumping",1446047236152,"0.767005","-0.114362","0.804128"
"user_001","Jumping",1446047236215,"-0.650847","-0.650847","-0.230521"
"user_001","Jumping",1446047236281,"3.56439","-5.90073","0.727487"
"user_001","Jumping",1446047236346,"7.05154","-17.97163","-1.61005"
"user_001","Jumping",1446047236410,"9.46572","-19.58108","2.10702"
"user_001","Jumping",1446047236475,"7.58802","-18.54643","3.10335"
"user_001","Jumping",1446047236540,"0.767005","-6.28393","0.689167"
"user_001","Jumping",1446047236604,"0.307161","2.29982","-0.498763"
"user_001","Jumping",1446047236669,"0.11556","-0.114362","-1.11189"
"user_001","Jumping",1446047236734,"2.2615","-1.45557","2.14534"
"user_001","Jumping",1446047236798,"1.80165","0.345482","0.765807"
"user_001","Jumping",1446047236863,"-0.650847","-0.305964","-1.15021"
"user_001","Jumping",1446047236928,"3.48775","-7.31858","-0.728685"
"user_001","Jumping",1446047236992,"5.32712","-18.92964","0.114362"
"user_001","Jumping",1446047237057,"10.34708","-19.58108","2.37526"
"user_001","Jumping",1446047237122,"5.97857","-17.78002","0.344284"
"user_001","Jumping",1446047237187,"2.8363","-3.25663","0.152682"
"user_001","Jumping",1446047237252,"-0.995729","3.37279","-1.64837"
"user_001","Jumping",1446047237317,"-1.64717","-0.650847","1.41725"
"user_001","Jumping",1446047237381,"1.30349","-0.152682","1.45557"
"user_001","Jumping",1446047237446,"2.79798","0.000599","-0.460442"
"user_001","Jumping",1446047237510,"1.41845","-0.459245","-1.38013"
"user_001","Jumping",1446047237575,"3.90927","-6.62882","-1.49509"
"user_001","Jumping",1446047237640,"4.98224","-19.27452","1.57053"
"user_001","Jumping",1446047237705,"12.22478","-19.58108","2.0687"
"user_001","Jumping",1446047237769,"4.5224","-16.74538","-0.383802"
"user_001","Jumping",1446047237834,"0.690364","-0.880768","-0.537083"
"user_001","Jumping",1446047237899,"1.26517","2.18486","-1.03525"
"user_001","Jumping",1446047237964,"2.6447","-0.037722","1.18733"
"user_001","Jumping",1446047238028,"2.56806","-0.114362","1.03405"
"user_001","Jumping",1446047238094,"-1.14901","0.11556","-0.307161"
"user_001","Jumping",1446047238157,"-0.574206","-0.114362","-0.920286"
"user_001","Jumping",1446047238223,"2.60638","-3.40991","-0.422122"
"user_001","Jumping",1446047238287,"6.32345","-17.62674","-0.728685"
"user_001","Jumping",1446047238352,"10.53868","-19.58108","0.919089"
"user_001","Jumping",1446047238417,"7.85626","-18.20155","0.995729"
"user_001","Jumping",1446047238481,"-0.152682","-1.41725","-1.22685"
"user_001","Jumping",1446047238546,"1.26517","2.22318","-1.87829"
"user_001","Jumping",1446047238611,"0.537083","-0.497565","1.76214"
"user_001","Jumping",1446047238676,"1.95493","0.230521","1.60885"
"user_001","Jumping",1446047238741,"0.920286","0.537083","-0.422122"
"user_001","Jumping",1446047238806,"0.000599","-0.650847","0.497565"
"user_001","Jumping",1446047238870,"1.64837","-1.99206","-1.72501"
"user_001","Jumping",1446047238935,"5.0972","-14.75272","-1.41845"
"user_001","Jumping",1446047239000,"10.50036","-19.58108","1.91542"
"user_001","Jumping",1446047239064,"8.16283","-19.58108","1.95374"
"user_001","Jumping",1446047239129,"3.56439","-9.4262","-1.22685"
"user_001","Jumping",1446047239194,"0.920286","2.79798","-1.34181"
"user_001","Jumping",1446047239259,"0.1922","0.652044","-0.537083"
"user_001","Jumping",1446047239324,"1.64837","-0.957409","1.41725"
"user_001","Jumping",1446047239388,"1.99325","-0.191003","0.957409"
"user_001","Jumping",1446047239453,"1.26517","-0.305964","-0.000599"
"user_001","Jumping",1446047239518,"2.4531","-4.17632","-1.34181"
"user_001","Jumping",1446047239583,"4.44576","-16.05561","-0.537083"
"user_001","Jumping",1446047239647,"9.58068","-19.58108","1.53221"
"user_001","Jumping",1446047239712,"8.04786","-19.2362","2.0687"
"user_001","Jumping",1446047239777,"1.80165","-6.01569","-0.422122"
"user_001","Jumping",1446047239841,"0.11556","2.10822","-2.6447"
"user_001","Jumping",1446047239906,"0.345482","-0.612526","-1.22685"
"user_001","Jumping",1446047239971,"1.45677","-0.880768","2.2603"
"user_001","Jumping",1446047240036,"0.843646","1.11189","-0.537083"
"user_001","Jumping",1446047240100,"0.996927","0.038919","-0.575403"
"user_001","Jumping",1446047240166,"3.29615","-3.98471","-0.422122"
"user_001","Jumping",1446047240231,"5.21216","-16.7837","-0.613724"
"user_001","Jumping",1446047240295,"7.39642","-19.58108","1.11069"
"user_001","Jumping",1446047240360,"10.23212","-19.58108","0.459245"
"user_001","Jumping",1446047240424,"1.80165","-12.14694","-1.22685"
"user_001","Jumping",1446047240489,"0.575403","1.83997","0.037722"
"user_001","Jumping",1446047240553,"-0.152682","2.22318","-3.0279"
"user_001","Jumping",1446047240618,"0.268841","-1.91542","3.06503"
"user_001","Jumping",1446047240683,"1.72501","-0.535886","1.83878"
"user_001","Jumping",1446047240748,"-1.18733","0.996927","-1.26517"
"user_001","Jumping",1446047240813,"0.920286","-0.535886","-1.91661"
"user_001","Jumping",1446047240878,"4.40743","-11.61046","0.459245"
"user_001","Jumping",1446047240941,"6.78329","-19.58108","4.82776"
"user_001","Jumping",1446047241007,"9.35075","-19.58108","5.74745"
"user_001","Jumping",1446047241072,"5.71033","-15.74905","-1.15021"
"user_001","Jumping",1446047241136,"-1.57053","-1.80046","-0.15388"
"user_001","Jumping",1446047241201,"-0.267643","2.18486","-2.14654"
"user_001","Jumping",1446047241266,"2.22318","-1.80046","1.80046"
"user_001","Jumping",1446047241330,"-1.34061","0.767005","-2.03158"
"user_001","Jumping",1446047241395,"-0.382604","-0.842448","0.382604"
"user_001","Jumping",1446047241459,"-0.765807","-1.41725","0.076042"
"user_001","Jumping",1446047241525,"5.97857","-10.34589","-1.49509"
"user_001","Jumping",1446047241589,"11.34341","-19.58108","6.13065"
"user_001","Jumping",1446047241654,"10.15548","-19.58108","8.58315"
"user_001","Jumping",1446047241718,"4.67568","-11.61046","-0.307161"
"user_001","Jumping",1446047241783,"-1.37893","-0.650847","0.459245"
"user_001","Jumping",1446047241849,"-0.919089","2.6447","-3.14286"
"user_001","Jumping",1446047241913,"1.07357","-1.03405","-0.613724"
"user_001","Jumping",1446047241977,"0.15388","-0.919089","2.18366"
"user_001","Jumping",1446047242042,"-0.995729","0.460442","0.305964"
"user_001","Jumping",1446047242107,"2.03158","-0.382604","0.076042"
"user_001","Jumping",1446047242172,"6.93658","-10.84405","-0.422122"
"user_001","Jumping",1446047242237,"13.79591","-19.58108","1.49389"
"user_001","Jumping",1446047242302,"15.86521","-19.50444","-1.72501"
"user_001","Jumping",1446047242366,"4.79064","-12.03198","1.8771"
"user_001","Jumping",1446047242431,"-0.497565","1.45677","-4.10087"
"user_001","Jumping",1446047242495,"0.11556","0.613724","-1.30349"
"user_001","Jumping",1446047242560,"-0.459245","-0.305964","2.56686"
"user_001","Jumping",1446047242625,"2.29982","1.18853","-0.767005"
"user_001","Jumping",1446047242690,"1.38013","-0.305964","-1.87829"
"user_001","Jumping",1446047242754,"2.52974","-2.75846","0.152682"
"user_001","Jumping",1446047242819,"5.32712","-13.21991","-1.34181"
"user_001","Jumping",1446047242884,"10.50036","-19.58108","1.8771"
"user_001","Jumping",1446047242948,"13.02951","-19.58108","-0.498763"
"user_001","Jumping",1446047243013,"4.33079","-10.34589","-2.4531"
"user_001","Jumping",1446047243078,"0.613724","0.498763","2.49022"
"user_001","Jumping",1446047243143,"0.307161","1.53341","-2.49142"
"user_001","Jumping",1446047243207,"0.077239","-0.344284","1.91542"
"user_001","Jumping",1446047243272,"2.03158","0.1922","-0.000599"
"user_001","Jumping",1446047243337,"1.22685","0.230521","-1.87829"
"user_001","Jumping",1446047243401,"0.537083","-1.26397","0.535886"
"user_001","Jumping",1446047243467,"5.2888","-11.22725","0.689167"
"user_001","Jumping",1446047243531,"11.57333","-19.58108","0.344284"
"user_001","Jumping",1446047243596,"14.524","-19.58108","2.33694"
"user_001","Jumping",1446047243661,"3.18118","-11.8787","0.191003"
"user_001","Jumping",1446047243725,"-1.07237","1.15021","0.152682"
"user_001","Jumping",1446047243790,"0.422122","1.95493","-1.87829"
"user_001","Jumping",1446047243855,"-0.535886","-0.957409","1.18733"
"user_001","Jumping",1446047243920,"3.60271","-0.114362","0.574206"
"user_001","Jumping",1446047243984,"2.87462","-0.535886","-0.268841"
"user_001","Jumping",1446047244049,"2.2615","-1.53221","-0.11556"
"user_001","Jumping",1446047244114,"6.85994","-10.61413","-1.11189"
"user_001","Jumping",1446047244178,"7.97122","-19.58108","-0.077239"
"user_001","Jumping",1446047244243,"14.86888","-19.58108","-1.41845"
"user_001","Jumping",1446047244308,"8.50771","-14.48448","-0.613724"
"user_001","Jumping",1446047244373,"-0.535886","-1.18733","1.64717"
"user_001","Jumping",1446047244437,"-4.5212","3.37279","0.191003"
"user_001","Jumping",1446047244502,"-1.72382","0.690364","0.191003"
"user_003","Jumping",1446047778034,"-2.75846","-7.28026","-1.45677"
"user_003","Jumping",1446047778099,"-3.75479","-7.08866","-2.37646"
"user_003","Jumping",1446047778164,"-2.14534","-6.74378","-2.22318"
"user_003","Jumping",1446047778229,"-2.22198","-6.01569","-2.2615"
"user_003","Jumping",1446047778293,"-3.63983","-9.04299","-2.6447"
"user_003","Jumping",1446047778358,"-4.82776","-17.09026","-4.02423"
"user_003","Jumping",1446047778422,"-5.82409","-19.46612","-6.70665"
"user_003","Jumping",1446047778488,"0.805325","-10.92069","-1.49509"
"user_003","Jumping",1446047778552,"-4.67448","1.22685","1.64717"
"user_003","Jumping",1446047778616,"-1.37893","0.460442","-2.18486"
"user_003","Jumping",1446047778682,"0.1922","-0.650847","-0.077239"
"user_003","Jumping",1446047778746,"-0.842448","0.11556","-1.26517"
"user_003","Jumping",1446047778811,"-1.26397","-11.91702","-3.64103"
"user_003","Jumping",1446047778876,"-1.41725","-19.58108","-0.767005"
"user_003","Jumping",1446047778940,"-1.76214","-15.44249","-2.68302"
"user_003","Jumping",1446047779006,"-0.574206","-9.00468","-1.76333"
"user_003","Jumping",1446047779071,"-3.14167","-4.36792","-1.68669"
"user_003","Jumping",1446047779135,"-3.37159","-4.3296","-2.4531"
"user_003","Jumping",1446047779200,"-4.06135","-4.75112","-3.10454"
"user_003","Jumping",1446047779265,"-4.36792","-11.26557","-0.345482"
"user_003","Jumping",1446047779329,"-5.97737","-19.12124","-4.25415"
"user_003","Jumping",1446047779394,"-3.75479","-19.19788","-4.9056"
"user_003","Jumping",1446047779459,"-0.459245","-7.39522","-0.537083"
"user_003","Jumping",1446047779524,"-2.91174","3.10454","-2.37646"
"user_003","Jumping",1446047779589,"-1.41725","-0.995729","-0.230521"
"user_003","Jumping",1446047779653,"0.422122","-0.114362","0.344284"
"user_003","Jumping",1446047779718,"-0.574206","-0.535886","-1.18853"
"user_003","Jumping",1446047779783,"-1.72382","-13.98632","-4.10087"
"user_003","Jumping",1446047779847,"-3.14167","-19.58108","-3.48775"
"user_003","Jumping",1446047779912,"-2.68182","-13.21991","-3.18118"
"user_003","Jumping",1446047779977,"-0.267643","-8.92803","-2.10822"
"user_003","Jumping",1446047780042,"-3.17999","-3.98471","-0.728685"
"user_003","Jumping",1446047780107,"-2.91174","-4.48288","-2.18486"
"user_003","Jumping",1446047780171,"-3.37159","-5.78577","-3.87095"
"user_003","Jumping",1446047780236,"-4.02303","-9.84772","-0.383802"
"user_003","Jumping",1446047780301,"-6.47553","-17.81835","-4.13919"
"user_003","Jumping",1446047780365,"-3.86975","-19.58108","-5.40376"
"user_003","Jumping",1446047780430,"-1.99206","-14.44616","-3.64103"
"user_003","Jumping",1446047780495,"-2.29862","-1.18733","-0.307161"
"user_003","Jumping",1446047780559,"-1.8771","1.99325","-1.68669"
"user_003","Jumping",1446047780625,"0.000599","-0.344284","0.650847"
"user_003","Jumping",1446047780689,"-0.459245","-0.191003","-0.613724"
"user_003","Jumping",1446047780754,"-2.60518","-6.9737","-4.714"
"user_003","Jumping",1446047780818,"-1.41725","-19.58108","-2.56806"
"user_003","Jumping",1446047780884,"-3.40991","-17.51178","-4.59904"
"user_003","Jumping",1446047780948,"-1.95374","-10.61413","-2.91294"
"user_003","Jumping",1446047781013,"-3.06503","-6.70546","-1.76333"
"user_003","Jumping",1446047781078,"-2.6435","-7.20362","-1.87829"
"user_003","Jumping",1446047781143,"-2.60518","-7.28026","-1.64837"
"user_003","Jumping",1446047781208,"-1.72382","-6.51385","-2.0699"
"user_003","Jumping",1446047781272,"-0.689167","-5.55585","-2.37646"
"user_003","Jumping",1446047781337,"-3.67815","-8.00835","-1.99325"
"user_003","Jumping",1446047781402,"-5.63249","-13.64143","-3.44943"
"user_003","Jumping",1446047781467,"-5.97737","-18.16323","-5.59536"
"user_003","Jumping",1446047781531,"-2.03038","-19.2362","-5.25048"
"user_003","Jumping",1446047781596,"-2.14534","-8.88971","-1.18853"
"user_003","Jumping",1446047781660,"-3.06503","2.52974","-0.767005"
"user_003","Jumping",1446047781725,"0.230521","0.268841","-0.345482"
"user_003","Jumping",1446047781790,"0.15388","-0.535886","-0.690364"
"user_003","Jumping",1446047781855,"-0.420925","-2.18366","-2.68302"
"user_003","Jumping",1446047781919,"-3.63983","-17.47346","-4.44576"
"user_003","Jumping",1446047781985,"-2.91174","-18.35483","-4.714"
"user_003","Jumping",1446047782049,"-0.919089","-10.88237","-2.2615"
"user_003","Jumping",1446047782114,"-3.02671","-6.93538","-2.68302"
"user_003","Jumping",1446047782178,"-2.75846","-7.3569","-2.10822"
"user_003","Jumping",1446047782244,"-1.45557","-7.85507","-1.22685"
"user_003","Jumping",1446047782309,"-1.8771","-6.32225","-1.99325"
"user_003","Jumping",1446047782373,"-1.64717","-5.90073","-2.33814"
"user_003","Jumping",1446047782438,"-2.49022","-8.08499","-1.80165"
"user_003","Jumping",1446047782503,"-4.40624","-11.26557","-2.37646"
"user_003","Jumping",1446047782568,"-5.13432","-17.1669","-4.67568"
"user_003","Jumping",1446047782632,"-3.40991","-19.54276","-5.71033"
"user_003","Jumping",1446047782697,"-1.99206","-13.48815","-4.06255"
"user_003","Jumping",1446047782762,"-2.22198","-1.68549","0.267643"
"user_003","Jumping",1446047782827,"-1.91542","1.80165","-1.68669"
"user_003","Jumping",1446047782891,"0.575403","-0.152682","0.459245"
"user_003","Jumping",1446047782956,"-0.842448","-0.804128","-1.03525"
"user_003","Jumping",1446047783021,"-1.76214","-12.22358","-5.67201"
"user_003","Jumping",1446047783086,"-2.33694","-19.19788","-4.02423"
"user_003","Jumping",1446047783151,"-1.14901","-14.98264","-4.13919"
"user_003","Jumping",1446047783215,"-2.22198","-9.04299","-2.91294"
"user_003","Jumping",1446047783280,"-2.41358","-5.59417","-0.613724"
"user_003","Jumping",1446047783344,"-2.60518","-5.78577","-2.33814"
"user_003","Jumping",1446047783409,"-3.67815","-4.44456","-2.4531"
"user_003","Jumping",1446047783474,"-2.8351","-4.63616","-3.75599"
"user_003","Jumping",1446047783539,"-1.64717","-16.4005","-0.843646"
"user_003","Jumping",1446047783604,"-6.62882","-19.58108","-8.58435"
"user_003","Jumping",1446047783669,"-1.72382","-14.67608","-3.52607"
"user_003","Jumping",1446047783733,"-1.57053","1.34181","0.612526"
"user_003","Jumping",1446047783798,"-1.18733","1.22685","-1.38013"
"user_003","Jumping",1446047783863,"-0.612526","-0.612526","-0.268841"
"user_003","Jumping",1446047783928,"-1.22565","0.345482","-0.805325"
"user_003","Jumping",1446047783992,"-1.11069","-2.2603","-2.56806"
"user_003","Jumping",1446047784057,"-2.8351","-17.62674","-5.02056"
"user_003","Jumping",1446047784122,"-3.90807","-19.19788","-5.59536"
"user_003","Jumping",1446047784187,"-1.72382","-12.6451","-3.64103"
"user_003","Jumping",1446047784252,"-1.49389","-6.7821","-2.0699"
"user_003","Jumping",1446047784316,"-2.14534","-4.67448","-1.15021"
"user_003","Jumping",1446047784381,"-2.91174","-6.93538","-2.6447"
"user_003","Jumping",1446047784446,"-3.71647","-5.86241","-2.56806"
"user_003","Jumping",1446047784510,"-0.344284","-6.51385","-2.8363"
"user_003","Jumping",1446047784575,"-4.02303","-14.98264","-2.2615"
"user_003","Jumping",1446047784639,"-5.36425","-19.58108","-8.89091"
"user_003","Jumping",1446047784704,"-0.191003","-14.906","-3.94759"
"user_003","Jumping",1446047784769,"-2.4519","0.077239","1.11069"
"user_003","Jumping",1446047784834,"-2.4519","1.22685","-1.41845"
"user_003","Jumping",1446047784899,"-0.344284","0.345482","-0.15388"
"user_003","Jumping",1446047784964,"-0.842448","0.422122","-0.996927"
"user_003","Jumping",1446047785029,"-2.29862","-4.3296","-4.63736"
"user_003","Jumping",1446047785093,"-0.765807","-18.92964","-3.98591"
"user_003","Jumping",1446047785158,"-4.3296","-19.38948","-5.17384"
"user_003","Jumping",1446047785222,"-1.11069","-12.6451","-1.22685"
"user_003","Jumping",1446047785287,"-3.44823","-7.24194","-2.18486"
"user_003","Jumping",1446047785352,"-2.49022","-6.51385","-2.95126"
"user_003","Jumping",1446047785417,"-2.10702","-6.85874","-1.22685"
"user_003","Jumping",1446047785482,"-2.79678","-7.05034","-2.14654"
"user_003","Jumping",1446047785546,"-2.56686","-5.01936","-2.52974"
"user_003","Jumping",1446047785611,"-2.87342","-6.62882","-2.56806"
"user_003","Jumping",1446047785676,"-4.63616","-14.44616","-2.52974"
"user_003","Jumping",1446047785741,"-5.67081","-19.58108","-6.59169"
"user_003","Jumping",1446047785805,"-3.67815","-17.66507","-6.63001"
"user_003","Jumping",1446047785870,"-0.919089","-4.82776","-0.268841"
"user_003","Jumping",1446047785934,"-2.91174","2.87462","-2.33814"
"user_003","Jumping",1446047785999,"-0.420925","-0.420925","0.919089"
"user_003","Jumping",1446047786065,"-0.037722","0.230521","0.382604"
"user_003","Jumping",1446047786129,"-0.842448","-0.497565","-3.0279"
"user_003","Jumping",1446047786194,"-0.995729","-15.48081","-4.33079"
"user_003","Jumping",1446047786259,"-3.98471","-19.50444","-6.89825"
"user_003","Jumping",1446047786324,"-0.574206","-13.29655","-3.94759"
"user_003","Jumping",1446047786388,"-1.41725","-8.85139","-1.38013"
"user_003","Jumping",1446047786453,"-3.94639","-5.59417","-3.14286"
"user_003","Jumping",1446047786518,"-2.18366","-8.04667","-3.06622"
"user_003","Jumping",1446047786582,"-1.60885","-8.92803","-1.15021"
"user_003","Jumping",1446047786647,"-2.72014","-5.13432","-2.33814"
"user_003","Jumping",1446047786712,"-2.03038","-4.25296","-3.18118"
"user_003","Jumping",1446047786777,"-3.48655","-9.84772","-1.45677"
"user_003","Jumping",1446047786841,"-6.01569","-18.96796","-6.78329"
"user_003","Jumping",1446047786906,"-4.44456","-19.4278","-8.62267"
"user_003","Jumping",1446047786970,"-0.267643","-8.92803","-1.57173"
"user_003","Jumping",1446047787035,"-2.91174","3.41111","-1.53341"
"user_003","Jumping",1446047787100,"0.268841","-0.765807","0.689167"
"user_003","Jumping",1446047787165,"-0.650847","0.383802","-0.728685"
"user_003","Jumping",1446047787230,"-0.880768","0.422122","-1.03525"
"user_003","Jumping",1446047787294,"-1.60885","-11.11229","-5.4804"
"user_003","Jumping",1446047787358,"-4.59784","-19.35116","-5.94025"
"user_003","Jumping",1446047787424,"-2.41358","-15.71073","-5.74865"
"user_003","Jumping",1446047787489,"-1.26397","-9.34956","-3.06622"
"user_003","Jumping",1446047787553,"-3.44823","-6.47553","-2.75966"
"user_003","Jumping",1446047787618,"-2.4519","-7.97003","-2.2615"
"user_003","Jumping",1446047787683,"-1.95374","-7.81675","-1.83997"
"user_003","Jumping",1446047787747,"-2.75846","-4.67448","-3.06622"
"user_003","Jumping",1446047787812,"-2.22198","-5.24928","-2.0699"
"user_003","Jumping",1446047787877,"-3.29495","-12.41518","-1.49509"
"user_003","Jumping",1446047787942,"-5.44089","-19.46612","-6.20849"
"user_003","Jumping",1446047788007,"-3.79311","-18.69972","-7.70298"
"user_003","Jumping",1446047788071,"-0.382604","-7.1653","-1.83997"
"user_003","Jumping",1446047788136,"-3.14167","2.72134","-0.575403"
"user_003","Jumping",1446047788201,"0.460442","-0.152682","0.114362"
"user_003","Jumping",1446047788265,"-0.842448","0.652044","-0.230521"
"user_003","Jumping",1446047788331,"-2.2603","-0.229323","-1.45677"
"user_003","Jumping",1446047788395,"-1.45557","-13.71807","-6.63001"
"user_003","Jumping",1446047788460,"-3.14167","-19.54276","-6.32345"
"user_003","Jumping",1446047788524,"-1.83878","-13.06663","-4.40743"
"user_003","Jumping",1446047788590,"-1.83878","-9.77108","-3.25783"
"user_003","Jumping",1446047788654,"-3.14167","-6.55217","-2.6447"
"user_003","Jumping",1446047788719,"-2.10702","-7.31858","-2.10822"
"user_003","Jumping",1446047788784,"-2.14534","-5.90073","-2.0699"
"user_003","Jumping",1446047788848,"-1.57053","-4.9044","-2.75966"
"user_003","Jumping",1446047788913,"-2.75846","-7.5485","-1.76333"
"user_003","Jumping",1446047788978,"-4.98104","-15.97897","-4.67568"
"user_003","Jumping",1446047789043,"-3.10335","-19.58108","-8.16283"
"user_003","Jumping",1446047789107,"-1.68549","-16.36218","-5.25048"
"user_003","Jumping",1446047789172,"-2.52854","-2.0687","-0.345482"
"user_003","Jumping",1446047789236,"-1.72382","2.41478","-2.37646"
"user_003","Jumping",1446047789301,"0.843646","-0.382604","1.11069"
"user_003","Jumping",1446047789366,"-0.689167","0.230521","-0.728685"
"user_003","Jumping",1446047789431,"-1.14901","-1.95374","-2.72134"
"user_003","Jumping",1446047789495,"-3.90807","-17.74171","-7.58802"
"user_003","Jumping",1446047789560,"-3.29495","-18.96796","-5.05888"
"user_003","Jumping",1446047789625,"-2.22198","-12.0703","-3.98591"
"user_003","Jumping",1446047789690,"-2.79678","-7.7401","-2.37646"
"user_003","Jumping",1446047789755,"-1.95374","-5.74745","-2.22318"
"user_003","Jumping",1446047789818,"-2.03038","-6.85874","-1.68669"
"user_003","Jumping",1446047789883,"-2.91174","-5.67081","-2.52974"
"user_003","Jumping",1446047789949,"-1.49389","-4.94272","-2.75966"
"user_003","Jumping",1446047790013,"-3.37159","-10.88237","-1.57173"
"user_003","Jumping",1446047790078,"-5.51753","-19.58108","-7.24314"
"user_003","Jumping",1446047790143,"-4.48288","-17.5501","-6.9749"
"user_003","Jumping",1446047790207,"-0.612526","-2.68182","-0.613724"
"user_003","Jumping",1446047790272,"-1.8771","2.68302","-2.03158"
"user_003","Jumping",1446047790337,"1.15021","-0.919089","1.64717"
"user_003","Jumping",1446047790402,"-2.03038","0.307161","-1.22685"
"user_003","Jumping",1446047790467,"-1.34061","-0.191003","-1.61005"
"user_003","Jumping",1446047790531,"-3.02671","-13.64143","-5.17384"
"user_003","Jumping",1446047790596,"-4.75112","-19.58108","-7.62634"
"user_003","Jumping",1446047790660,"-2.60518","-15.05928","-6.01689"
"user_003","Jumping",1446047790726,"-1.26397","-8.12331","-3.10454"
"user_003","Jumping",1446047790790,"-3.25663","-5.97737","-3.0279"
"user_003","Jumping",1446047790855,"-0.420925","-6.24561","-2.2615"
"user_003","Jumping",1446047790919,"-1.83878","-3.40991","-3.60271"
"user_003","Jumping",1446047790984,"-3.94639","-5.36425","-3.75599"
"user_003","Jumping",1446047791049,"-2.2603","-13.98632","-3.67935"
"user_003","Jumping",1446047791114,"-7.70178","-19.58108","-7.5497"
"user_003","Jumping",1446047791179,"-2.52854","-15.36585","-6.66833"
"user_003","Jumping",1446047791243,"-0.574206","-0.497565","-0.230521"
"user_003","Jumping",1446047791308,"-2.0687","0.958607","-0.575403"
"user_003","Jumping",1446047791373,"0.11556","-0.497565","0.344284"
"user_003","Jumping",1446047791438,"-1.30229","1.34181","-1.11189"
"user_003","Jumping",1446047791503,"-0.382604","-0.880768","-2.22318"
"user_003","Jumping",1446047791568,"-2.87342","-15.97897","-6.28513"
"user_003","Jumping",1446047791632,"-2.95007","-19.38948","-7.51138"
"user_003","Jumping",1446047791697,"-4.59784","-13.37319","-5.02056"
"user_003","Jumping",1446047791762,"-2.14534","-9.84772","-3.2195"
"user_003","Jumping",1446047791827,"-2.29862","-6.55217","-2.49142"
"user_003","Jumping",1446047791891,"-1.68549","-7.47186","-2.29982"
"user_003","Jumping",1446047791956,"-1.22565","-8.16163","-2.56806"
"user_003","Jumping",1446047792021,"-2.95007","-5.096","-2.52974"
"user_003","Jumping",1446047792085,"-4.02303","-4.06135","-7.7413"
"user_003","Jumping",1446047792151,"-2.60518","-14.40784","0.727487"
"user_003","Jumping",1446047792215,"-6.24561","-19.58108","-8.89091"
"user_003","Jumping",1446047792280,"-1.60885","-12.56846","-3.2195"
"user_003","Jumping",1446047792344,"-3.10335","3.14286","-1.26517"
"user_003","Jumping",1446047792410,"-0.037722","0.000599","-0.11556"
"user_003","Jumping",1446047792474,"0.268841","-0.650847","0.114362"
"user_003","Jumping",1446047792539,"-2.68182","0.996927","-1.99325"
"user_003","Jumping",1446047792603,"-1.64717","-4.67448","-5.51872"
"user_003","Jumping",1446047792669,"-2.87342","-18.96796","-5.86361"
"user_003","Jumping",1446047792733,"-3.29495","-18.66139","-4.44576"
"user_003","Jumping",1446047792798,"-4.02303","-13.21991","-4.79064"
"user_003","Jumping",1446047792863,"-2.95007","-7.97003","-2.79798"
"user_003","Jumping",1446047792928,"-3.17999","-6.20729","-2.29982"
"user_003","Jumping",1446047792992,"-3.25663","-5.40257","-2.37646"
"user_003","Jumping",1446047793057,"-3.40991","-4.5212","-3.18118"
"user_003","Jumping",1446047793122,"-3.29495","-3.90807","-3.94759"
"user_003","Jumping",1446047793186,"-4.7128","-14.7144","-2.75966"
"user_003","Jumping",1446047793251,"-4.55952","-19.58108","-7.77962"
"user_003","Jumping",1446047793316,"-2.95007","-16.32385","-6.93658"
"user_003","Jumping",1446047793380,"-1.26397","-2.14534","-1.38013"
"user_003","Jumping",1446047793445,"-2.10702","2.33814","-1.64837"
"user_003","Jumping",1446047793510,"-0.420925","-0.267643","1.07237"
"user_003","Jumping",1446047793575,"-0.995729","0.383802","-0.537083"
"user_003","Jumping",1446047793640,"-1.14901","-1.76214","-2.29982"
"user_003","Jumping",1446047793704,"-2.56686","-14.82936","-6.28513"
"user_003","Jumping",1446047793768,"-3.40991","-19.31284","-7.3581"
"user_003","Jumping",1446047793834,"-3.52487","-13.87135","-5.63368"
"user_003","Jumping",1446047793899,"-2.68182","-10.84405","-3.10454"
"user_003","Jumping",1446047793963,"-2.72014","-4.78944","-2.72134"
"user_003","Jumping",1446047794028,"-1.03405","-4.94272","-1.68669"
"user_003","Jumping",1446047794093,"-2.10702","-5.93905","-2.14654"
"user_003","Jumping",1446047794158,"-1.57053","-5.90073","-3.2195"
"user_003","Jumping",1446047794222,"-4.3296","-8.08499","-1.15021"
"user_003","Jumping",1446047794287,"-4.48288","-19.08292","-6.36177"
"user_003","Jumping",1446047794352,"-4.67448","-19.58108","-8.27779"
"user_003","Jumping",1446047794416,"0.000599","-10.76741","-2.33814"
"user_003","Jumping",1446047794481,"-1.95374","3.41111","-1.07357"
"user_003","Jumping",1446047794546,"-0.152682","-0.689167","0.229323"
"user_003","Jumping",1446047794611,"-0.957409","0.422122","-0.460442"
"user_003","Jumping",1446047794676,"-0.957409","0.996927","-0.881966"
"user_003","Jumping",1446047794740,"-1.57053","-3.60151","-4.75232"
"user_003","Jumping",1446047794805,"-1.99206","-18.35483","-5.78697"
"user_003","Jumping",1446047794870,"-3.71647","-19.2362","-6.47673"
"user_003","Jumping",1446047794935,"-0.842448","-14.94432","-4.17751"
"user_002","Standing",1446309439342,"-2.49022","-9.19628","-1.11189"
"user_002","Standing",1446309439349,"-2.41358","-9.15796","-1.22685"
"user_002","Standing",1446309439358,"-2.56686","-9.15796","-1.30349"
"user_002","Standing",1446309439365,"-2.75846","-9.08132","-1.11189"
"user_002","Standing",1446309439373,"-2.75846","-9.08132","-1.15021"
"user_002","Standing",1446309439382,"-2.8351","-9.15796","-0.920286"
"user_002","Standing",1446309439390,"-2.8357","-9.15855","-0.919687"
"user_002","Standing",1446309439398,"-2.95007","-9.2346","-0.881966"
"user_002","Standing",1446309439406,"-2.8351","-9.11964","-0.958607"
"user_002","Standing",1446309439414,"-2.8351","-8.96635","-1.15021"
"user_002","Standing",1446309439422,"-2.95007","-9.08132","-0.920286"
"user_002","Standing",1446309439430,"-2.95007","-8.88971","-0.996927"
"user_002","Standing",1446309439438,"-2.91174","-9.00468","-1.15021"
"user_002","Standing",1446309439447,"-3.02671","-8.96635","-0.996927"
"user_002","Standing",1446309439454,"-2.79678","-8.96635","-1.15021"
"user_002","Standing",1446309439463,"-2.87342","-9.08132","-1.34181"
"user_002","Standing",1446309439471,"-2.98839","-9.19628","-1.22685"
"user_002","Standing",1446309439479,"-2.95007","-9.00468","-1.30349"
"user_002","Standing",1446309439487,"-2.98839","-9.00468","-1.15021"
"user_002","Standing",1446309439495,"-3.06503","-9.00468","-0.958607"
"user_002","Standing",1446309439503,"-3.02671","-9.04299","-0.881966"
"user_002","Standing",1446309439511,"-2.91174","-9.00468","-0.920286"
"user_002","Standing",1446309439519,"-2.95007","-9.08132","-0.767005"
"user_002","Standing",1446309439527,"-2.8351","-9.00468","-0.958607"
"user_002","Standing",1446309439536,"-2.95007","-9.00468","-0.996927"
"user_002","Standing",1446309439543,"-2.75846","-9.04299","-0.690364"
"user_002","Standing",1446309439552,"-2.6435","-9.00468","-1.03525"
"user_002","Standing",1446309439560,"-2.72014","-9.00468","-1.15021"
"user_002","Standing",1446309439568,"-2.68182","-9.04299","-1.11189"
"user_002","Standing",1446309439576,"-2.60518","-9.00468","-1.11189"
"user_002","Standing",1446309439584,"-2.52854","-8.88971","-1.15021"
"user_002","Standing",1446309439593,"-2.6435","-8.92803","-1.03525"
"user_002","Standing",1446309439601,"-2.60518","-8.96635","-0.996927"
"user_002","Standing",1446309439609,"-2.6435","-9.04299","-0.996927"
"user_002","Standing",1446309439616,"-2.75846","-9.04299","-0.920286"
"user_002","Standing",1446309439624,"-2.6435","-9.19628","-0.805325"
"user_002","Standing",1446309439633,"-2.79678","-8.96635","-0.767005"
"user_002","Standing",1446309439641,"-2.87342","-8.92803","-0.958607"
"user_002","Standing",1446309439649,"-2.60518","-9.11964","-0.843646"
"user_002","Standing",1446309439657,"-2.8351","-9.08132","-0.843646"
"user_002","Standing",1446309439665,"-2.8351","-9.2346","-0.920286"
"user_002","Standing",1446309439674,"-2.72014","-9.11964","-0.958607"
"user_002","Standing",1446309439682,"-2.87342","-9.15796","-1.18853"
"user_002","Standing",1446309439690,"-3.06503","-9.2346","-1.18853"
"user_002","Standing",1446309439698,"-2.8351","-9.08132","-0.996927"
"user_002","Standing",1446309439705,"-2.98839","-9.04299","-1.03525"
"user_002","Standing",1446309439713,"-3.17999","-8.96635","-1.18853"
"user_002","Standing",1446309439722,"-3.21831","-8.88971","-1.18853"
"user_002","Standing",1446309439729,"-3.17999","-8.92803","-1.15021"
"user_002","Standing",1446309439738,"-3.17999","-8.77475","-1.22685"
"user_002","Standing",1446309439746,"-3.33327","-8.65979","-1.07357"
"user_002","Standing",1446309439754,"-3.37159","-8.58315","-1.34181"
"user_002","Standing",1446309439762,"-3.33327","-8.77475","-1.18853"
"user_002","Standing",1446309439771,"-3.33327","-8.58315","-1.07357"
"user_002","Standing",1446309439779,"-3.14167","-8.92803","-1.03525"
"user_002","Standing",1446309439787,"-3.25663","-8.85139","-0.881966"
"user_002","Standing",1446309439795,"-3.10335","-8.85139","-0.920286"
"user_002","Standing",1446309439803,"-2.87342","-8.85139","-0.843646"
"user_002","Standing",1446309439811,"-2.91174","-8.92803","-0.767005"
"user_002","Standing",1446309439819,"-2.87342","-8.88971","-0.805325"
"user_002","Standing",1446309439827,"-2.98839","-8.96635","-0.767005"
"user_002","Standing",1446309439835,"-2.79678","-9.11964","-1.07357"
"user_002","Standing",1446309439843,"-2.87342","-9.08132","-0.920286"
"user_002","Standing",1446309439851,"-2.95007","-9.15796","-0.805325"
"user_002","Standing",1446309439859,"-3.02671","-8.85139","-0.728685"
"user_002","Standing",1446309439868,"-2.98839","-8.92803","-0.690364"
"user_002","Standing",1446309439875,"-2.98839","-8.96635","-0.690364"
"user_002","Standing",1446309439883,"-2.91174","-8.96635","-0.881966"
"user_002","Standing",1446309439892,"-3.02671","-8.85139","-0.613724"
"user_002","Standing",1446309439900,"-3.06503","-9.04299","-0.767005"
"user_002","Standing",1446309439908,"-2.87342","-8.73643","-0.652044"
"user_002","Standing",1446309439916,"-2.95007","-8.88971","-0.728685"
"user_002","Standing",1446309439924,"-3.10335","-8.77475","-0.690364"
"user_002","Standing",1446309439932,"-2.91174","-8.77475","-0.652044"
"user_002","Standing",1446309439940,"-2.91174","-9.04299","-0.805325"
"user_002","Standing",1446309439948,"-2.91174","-9.04299","-0.767005"
"user_002","Standing",1446309439957,"-3.02671","-9.04299","-0.652044"
"user_002","Standing",1446309439965,"-3.06503","-9.27292","-0.805325"
"user_002","Standing",1446309439973,"-3.14167","-9.00468","-0.767005"
"user_002","Standing",1446309439980,"-2.95007","-8.96635","-0.843646"
"user_002","Standing",1446309439989,"-3.10335","-9.00468","-1.15021"
"user_002","Standing",1446309439997,"-2.98839","-9.19628","-1.03525"
"user_002","Standing",1446309440004,"-3.10335","-9.19628","-1.15021"
"user_002","Standing",1446309440013,"-2.91174","-9.11964","-1.18853"
"user_002","Standing",1446309440021,"-2.91174","-9.08132","-1.22685"
"user_002","Standing",1446309440029,"-2.95007","-9.00468","-1.26517"
"user_002","Standing",1446309440038,"-3.06503","-9.08132","-1.15021"
"user_002","Standing",1446309440045,"-3.06503","-9.00468","-1.03525"
"user_002","Standing",1446309440054,"-3.10335","-9.11964","-1.07357"
"user_002","Standing",1446309440062,"-3.10335","-8.96635","-0.996927"
"user_002","Standing",1446309440069,"-3.10335","-8.96635","-1.03525"
"user_002","Standing",1446309440078,"-3.17999","-9.00468","-1.11189"
"user_002","Standing",1446309440086,"-3.14167","-8.85139","-0.996927"
"user_002","Standing",1446309440094,"-3.17999","-9.00468","-0.728685"
"user_002","Standing",1446309440102,"-3.17999","-8.96635","-0.958607"
"user_002","Standing",1446309440111,"-3.10335","-9.00468","-0.881966"
"user_002","Standing",1446309440119,"-3.17999","-9.00468","-1.03525"
"user_002","Standing",1446309440126,"-3.02671","-9.00468","-0.881966"
"user_002","Standing",1446309440135,"-3.06503","-9.00468","-0.728685"
"user_002","Standing",1446309440142,"-3.21831","-8.92803","-1.03525"
"user_002","Standing",1446309440151,"-3.33327","-8.85139","-0.767005"
"user_002","Standing",1446309440158,"-3.21831","-9.04299","-0.652044"
"user_002","Standing",1446309440167,"-3.33327","-8.85139","-0.613724"
"user_002","Standing",1446309440175,"-3.37159","-8.85139","-0.345482"
"user_002","Standing",1446309440183,"-3.37159","-9.00468","-0.652044"
"user_002","Standing",1446309440192,"-3.33327","-8.81307","-0.460442"
"user_002","Standing",1446309440199,"-3.21831","-9.08132","-0.537083"
"user_002","Standing",1446309440208,"-3.21831","-8.92803","-0.690364"
"user_002","Standing",1446309440215,"-3.14167","-8.96635","-0.575403"
"user_002","Standing",1446309440224,"-3.17999","-8.92803","-0.690364"
"user_002","Standing",1446309440232,"-3.17999","-8.77475","-0.690364"
"user_002","Standing",1446309440239,"-3.14167","-8.88971","-0.805325"
"user_002","Standing",1446309440248,"-3.10335","-9.04299","-0.843646"
"user_002","Standing",1446309440255,"-3.14167","-8.88971","-0.767005"
"user_002","Standing",1446309440264,"-3.06503","-9.11964","-0.805325"
"user_002","Standing",1446309440272,"-3.14167","-8.96635","-0.690364"
"user_002","Standing",1446309440280,"-3.29495","-9.08132","-0.843646"
"user_002","Standing",1446309440288,"-3.33327","-8.81307","-0.575403"
"user_002","Standing",1446309440296,"-3.21831","-8.88971","-0.575403"
"user_002","Standing",1446309440305,"-3.21831","-8.96635","-0.613724"
"user_002","Standing",1446309440312,"-3.14167","-8.77475","-0.537083"
"user_002","Standing",1446309440320,"-3.10335","-8.85139","-0.613724"
"user_002","Standing",1446309440329,"-3.21831","-9.00468","-0.613724"
"user_002","Standing",1446309440337,"-3.14167","-8.85139","-0.613724"
"user_002","Standing",1446309440345,"-3.21831","-9.04299","-0.690364"
"user_002","Standing",1446309440353,"-3.06503","-8.92803","-0.575403"
"user_002","Standing",1446309440361,"-3.25663","-9.11964","-0.728685"
"user_002","Standing",1446309440369,"-3.21831","-8.92803","-0.652044"
"user_002","Standing",1446309440377,"-3.06503","-8.92803","-0.843646"
"user_002","Standing",1446309440385,"-3.06503","-9.04299","-0.690364"
"user_002","Standing",1446309440394,"-3.21831","-9.00468","-0.460442"
"user_002","Standing",1446309440402,"-3.02671","-8.92803","-0.652044"
"user_002","Standing",1446309440410,"-3.21831","-8.96635","-0.652044"
"user_002","Standing",1446309440417,"-3.25663","-8.96635","-0.767005"
"user_002","Standing",1446309440426,"-3.21831","-8.88971","-0.728685"
"user_002","Standing",1446309440434,"-3.37159","-8.85139","-0.767005"
"user_002","Standing",1446309440443,"-3.21831","-8.85139","-0.537083"
"user_002","Standing",1446309440450,"-3.10335","-9.11964","-0.767005"
"user_002","Standing",1446309440458,"-3.10335","-9.19628","-0.920286"
"user_002","Standing",1446309440467,"-3.10335","-9.00468","-0.767005"
"user_002","Standing",1446309440474,"-3.02671","-8.96635","-0.767005"
"user_002","Standing",1446309440482,"-3.10335","-8.92803","-0.805325"
"user_002","Standing",1446309440491,"-3.17999","-8.92803","-0.843646"
"user_002","Standing",1446309440498,"-3.33327","-8.96635","-0.805325"
"user_002","Standing",1446309440506,"-3.29495","-8.85139","-0.575403"
"user_002","Standing",1446309440515,"-3.21831","-8.88971","-0.728685"
"user_002","Standing",1446309440523,"-3.29495","-8.92803","-0.652044"
"user_002","Standing",1446309440531,"-3.37159","-9.04299","-0.575403"
"user_002","Standing",1446309440539,"-3.33327","-8.92803","-0.613724"
"user_002","Standing",1446309440547,"-3.33327","-8.88971","-0.498763"
"user_002","Standing",1446309440555,"-3.21831","-9.08132","-0.690364"
"user_002","Standing",1446309440564,"-3.06503","-8.88971","-0.652044"
"user_002","Standing",1446309440571,"-3.17999","-8.88971","-0.537083"
"user_002","Standing",1446309440580,"-3.06503","-8.88971","-0.498763"
"user_002","Standing",1446309440587,"-3.10335","-8.85139","-0.575403"
"user_002","Standing",1446309440596,"-3.06503","-9.08132","-0.613724"
"user_002","Standing",1446309440604,"-2.87342","-8.85139","-0.652044"
"user_002","Standing",1446309440612,"-2.95007","-9.08132","-0.728685"
"user_002","Standing",1446309440620,"-3.14167","-8.96635","-0.422122"
"user_002","Standing",1446309440628,"-3.02671","-8.92803","-0.537083"
"user_002","Standing",1446309440636,"-3.14167","-9.00468","-0.422122"
"user_002","Standing",1446309440645,"-3.10335","-9.08132","-0.383802"
"user_002","Standing",1446309440653,"-3.14167","-8.81307","-0.307161"
"user_002","Standing",1446309440660,"-3.17999","-8.85139","-0.422122"
"user_002","Standing",1446309440669,"-3.21831","-8.85139","-0.1922"
"user_002","Standing",1446309440676,"-3.17999","-9.04299","-0.498763"
"user_002","Standing",1446309440685,"-3.02671","-9.04299","-0.460442"
"user_002","Standing",1446309440693,"-3.21831","-8.85139","-0.498763"
"user_002","Standing",1446309440701,"-3.10335","-9.08132","-0.498763"
"user_002","Standing",1446309440709,"-3.29495","-8.96635","-0.537083"
"user_002","Standing",1446309440717,"-3.06503","-8.88971","-0.383802"
"user_002","Standing",1446309440725,"-3.10335","-9.15796","-0.498763"
"user_002","Standing",1446309440734,"-2.91174","-9.00468","-0.345482"
"user_002","Standing",1446309440741,"-3.17999","-8.88971","-0.498763"
"user_002","Standing",1446309440749,"-3.21831","-9.08132","-0.537083"
"user_002","Standing",1446309440757,"-3.06503","-9.00468","-0.460442"
"user_002","Standing",1446309440766,"-3.06503","-9.00468","-0.613724"
"user_002","Standing",1446309440774,"-3.10335","-8.92803","-0.498763"
"user_002","Standing",1446309440782,"-3.25663","-8.92803","-0.613724"
"user_002","Standing",1446309440790,"-3.17999","-8.92803","-0.728685"
"user_002","Standing",1446309440798,"-3.29495","-9.04299","-0.422122"
"user_002","Standing",1446309440806,"-3.17999","-9.08132","-0.422122"
"user_002","Standing",1446309440814,"-3.21831","-9.00468","-0.460442"
"user_002","Standing",1446309440822,"-3.06503","-8.96635","-0.460442"
"user_002","Standing",1446309440831,"-3.17999","-9.04299","-0.537083"
"user_002","Standing",1446309440839,"-3.14167","-9.04299","-0.498763"
"user_002","Standing",1446309440847,"-3.17999","-9.08132","-0.345482"
"user_002","Standing",1446309440855,"-3.21831","-9.08132","-0.613724"
"user_002","Standing",1446309440863,"-3.33327","-9.15796","-0.460442"
"user_002","Standing",1446309440871,"-3.37159","-9.00468","-0.460442"
"user_002","Standing",1446309440879,"-3.17999","-8.92803","-0.537083"
"user_002","Standing",1446309440887,"-3.17999","-8.96635","-0.345482"
"user_002","Standing",1446309440896,"-3.17999","-9.04299","-0.383802"
"user_002","Standing",1446309440904,"-3.37159","-9.11964","-0.345482"
"user_002","Standing",1446309440912,"-3.33327","-9.04299","-0.460442"
"user_002","Standing",1446309440920,"-3.44823","-8.96635","-0.460442"
"user_002","Standing",1446309440927,"-3.25663","-8.81307","-0.345482"
"user_002","Standing",1446309440936,"-3.25663","-8.92803","-0.460442"
"user_002","Standing",1446309440944,"-3.40991","-8.85139","-0.652044"
"user_002","Standing",1446309440951,"-3.21831","-8.85139","-0.575403"
"user_002","Standing",1446309440960,"-3.33327","-8.85139","-0.498763"
"user_002","Standing",1446309440968,"-3.37159","-8.85139","-0.460442"
"user_002","Standing",1446309440976,"-3.17999","-8.81307","-0.728685"
"user_002","Standing",1446309440985,"-2.98839","-8.88971","-0.575403"
"user_002","Standing",1446309440992,"-3.06503","-8.85139","-0.613724"
"user_002","S...

ScaDaMaLe Course site and book

Community Packages in Spark - more generally

Let us recall the following quoate in Chapter 10 of High Performance Spark book (needs access to Orielly publishers via your library/subscription): - https://learning.oreilly.com/library/view/high-performance-spark/9781491943199/ch10.html#components

Beyond the integrated components, the community packages can add important functionality to Spark, sometimes even superseding built-in functionality—like with GraphFrames.

Here we introduce you to GraphFrames quickly so you don't need to drop down to the GraphX library that requires more understanding of caching and checkpointing to keep the vertex program's DAG from exploding or becoming inefficient.

GraphFrames User Guide (Scala)

GraphFrames is a package for Apache Spark which provides DataFrame-based Graphs. It provides high-level APIs in Scala, Java, and Python. It aims to provide both the functionality of GraphX and extended functionality taking advantage of Spark DataFrames. This extended functionality includes motif finding, DataFrame-based serialization, and highly expressive graph queries.

The GraphFrames package is available from Spark Packages.

This notebook demonstrates examples from the GraphFrames User Guide: https://graphframes.github.io/graphframes/docs/_site/user-guide.html.

sc.version // link the right library depending on Spark version of the cluster that's running
// spark version 2.3.0 works with graphframes:graphframes:0.7.0-spark2.3-s_2.11
// spark version 3.0.1 works with graphframes:graphframes:0.8.1-spark3.0-s_2.12
res0: String = 3.1.2

Since databricks.com stopped allowing IFrame embeds we have to open it in a separate window now. The blog is insightful and worth a perusal:

  • https://databricks.com/blog/2016/03/03/introducing-graphframes.html
// we first need to install the library - graphframes as a Spark package - and attach it to our cluster - see note two cells above!
import org.apache.spark.sql._
import org.apache.spark.sql.functions._

import org.graphframes._
import org.apache.spark.sql._
import org.apache.spark.sql.functions._
import org.graphframes._

Creating GraphFrames

Let us try to create an example social network from the blog: * https://databricks.com/blog/2016/03/03/introducing-graphframes.html.

Users can create GraphFrames from vertex and edge DataFrames.

  • Vertex DataFrame: A vertex DataFrame should contain a special column named id which specifies unique IDs for each vertex in the graph.
  • Edge DataFrame: An edge DataFrame should contain two special columns: src (source vertex ID of edge) and dst (destination vertex ID of edge).

Both DataFrames can have arbitrary other columns. Those columns can represent vertex and edge attributes.

In our example, we can use a GraphFrame can store data or properties associated with each vertex and edge.

In our social network, each user might have an age and name, and each connection might have a relationship type.

Create the vertices and edges

// Vertex DataFrame
val v = sqlContext.createDataFrame(List(
  ("a", "Alice", 34),
  ("b", "Bob", 36),
  ("c", "Charlie", 30),
  ("d", "David", 29),
  ("e", "Esther", 32),
  ("f", "Fanny", 36),
  ("g", "Gabby", 60)
)).toDF("id", "name", "age")

// Edge DataFrame
val e = sqlContext.createDataFrame(List(
  ("a", "b", "friend"),
  ("b", "c", "follow"),
  ("c", "b", "follow"),
  ("f", "c", "follow"),
  ("e", "f", "follow"),
  ("e", "d", "friend"),
  ("d", "a", "friend"),
  ("a", "e", "friend")
)).toDF("src", "dst", "relationship")
v: org.apache.spark.sql.DataFrame = [id: string, name: string ... 1 more field]
e: org.apache.spark.sql.DataFrame = [src: string, dst: string ... 1 more field]

Let's create a graph from these vertices and these edges:

val g = GraphFrame(v, e)
g: org.graphframes.GraphFrame = GraphFrame(v:[id: string, name: string ... 1 more field], e:[src: string, dst: string ... 1 more field])

Let's use the d3.graphs to visualise graphs (recall the D3 graphs in wiki-click example). You need the Run Cell below using that cell's Play button's drop-down menu.

Warning: classes defined within packages cannot be redefined without a cluster restart.
Compilation successful.
d3.graphs.help()

Produces a force-directed graph given a collection of edges of the following form:
case class Edge(src: String, dest: String, count: Long)

Usage:
import d3._
graphs.force(
  height = 500,
  width = 500,
  clicks: Dataset[Edge])

import org.apache.spark.sql.functions.lit // import the lit function in sql
val gE= g.edges.select($"src", $"dst".as("dest"), lit(1L).as("count")) // for us the column count is just an edge incidence
import org.apache.spark.sql.functions.lit
gE: org.apache.spark.sql.DataFrame = [src: string, dest: string ... 1 more field]
display(gE)
src dest count
a b 1.0
b c 1.0
c b 1.0
f c 1.0
e f 1.0
e d 1.0
d a 1.0
a e 1.0
d3.graphs.force(
  height = 500,
  width = 500,
  clicks = gE.as[d3.Edge])

// This example graph also comes with the GraphFrames package.
val g0 = examples.Graphs.friends
g0: org.graphframes.GraphFrame = GraphFrame(v:[id: string, name: string ... 1 more field], e:[src: string, dst: string ... 1 more field])
d3.graphs.force( // let us see g0 now in one cell
  height = 500,
  width = 500,
  clicks = g0.edges.select($"src", $"dst".as("dest"), lit(1L).as("count")).as[d3.Edge])

Basic graph and DataFrame queries

GraphFrames provide several simple graph queries, such as node degree.

Also, since GraphFrames represent graphs as pairs of vertex and edge DataFrames, it is easy to make powerful queries directly on the vertex and edge DataFrames. Those DataFrames are made available as vertices and edges fields in the GraphFrame.

Simple queries are simple

GraphFrames make it easy to express queries over graphs. Since GraphFrame vertices and edges are stored as DataFrames, many queries are just DataFrame (or SQL) queries.

display(g.vertices)
id name age
a Alice 34.0
b Bob 36.0
c Charlie 30.0
d David 29.0
e Esther 32.0
f Fanny 36.0
g Gabby 60.0
display(g0.vertices) // this is the same query on the graph loaded as an example from GraphFrame package
id name age
a Alice 34.0
b Bob 36.0
c Charlie 30.0
d David 29.0
e Esther 32.0
f Fanny 36.0
g Gabby 60.0
display(g.edges)
src dst relationship
a b friend
b c follow
c b follow
f c follow
e f follow
e d friend
d a friend
a e friend

The incoming degree of the vertices:

display(g.inDegrees)
id inDegree
c 2.0
d 1.0
e 1.0
b 2.0
f 1.0
a 1.0

The outgoing degree of the vertices:

display(g.outDegrees)
id outDegree
a 2.0
c 1.0
e 2.0
d 1.0
b 1.0
f 1.0

The degree of the vertices:

display(g.degrees)
id degree
b 3.0
a 3.0
c 3.0
f 2.0
e 3.0
d 2.0

You can run queries directly on the vertices DataFrame. For example, we can find the age of the youngest person in the graph:

val youngest = g.vertices.groupBy().min("age")
display(youngest)
min(age)
29.0

Likewise, you can run queries on the edges DataFrame.

For example, let us count the number of 'follow' relationships in the graph:

val numFollows = g.edges.filter("relationship = 'follow'").count()
numFollows: Long = 4

Motif finding

More complex relationships involving edges and vertices can be built using motifs.

The following cell finds the pairs of vertices with edges in both directions between them.

The result is a dataframe, in which the column names are given by the motif keys.

Check out the GraphFrame User Guide at https://graphframes.github.io/graphframes/docs/_site/user-guide.html for more details on the API.

// Search for pairs of vertices with edges in both directions between them, i.e., find undirected or bidirected edges.
val motifs = g.find("(a)-[e1]->(b); (b)-[e2]->(a)")
display(motifs)

Since the result is a DataFrame, more complex queries can be built on top of the motif.

Let us find all the reciprocal relationships in which one person is older than 30:

val filtered = motifs.filter("b.age > 30")
display(filtered)

You Try!

//Search for all "directed triangles" or triplets of vertices: a,b,c with edges: a->b, b->c and c->a
//uncomment the next 2 lines and replace the "XXX" below
//val motifs3 = g.find("(a)-[e1]->(b); (b)-[e2]->(c); (c)-[e3]->(XXX)")
//display(motifs3)

Stateful queries

Many motif queries are stateless and simple to express, as in the examples above. The next examples demonstrate more complex queries which carry state along a path in the motif. These queries can be expressed by combining GraphFrame motif finding with filters on the result, where the filters use sequence operations to construct a series of DataFrame Columns.

For example, suppose one wishes to identify a chain of 4 vertices with some property defined by a sequence of functions. That is, among chains of 4 vertices a->b->c->d, identify the subset of chains matching this complex filter:

  • Initialize state on path.
  • Update state based on vertex a.
  • Update state based on vertex b.
  • Etc. for c and d.
  • If final state matches some condition, then the chain is accepted by the filter.

The below code snippets demonstrate this process, where we identify chains of 4 vertices such that at least 2 of the 3 edges are friend relationships. In this example, the state is the current count of friend edges; in general, it could be any DataFrame Column.

// Find chains of 4 vertices.
val chain4 = g.find("(a)-[ab]->(b); (b)-[bc]->(c); (c)-[cd]->(d)")

// Query on sequence, with state (cnt)
//  (a) Define method for updating state given the next element of the motif.
def sumFriends(cnt: Column, relationship: Column): Column = {
  when(relationship === "friend", cnt + 1).otherwise(cnt)
}
//  (b) Use sequence operation to apply method to sequence of elements in motif.
//      In this case, the elements are the 3 edges.
val condition = Seq("ab", "bc", "cd").
  foldLeft(lit(0))((cnt, e) => sumFriends(cnt, col(e)("relationship")))
//  (c) Apply filter to DataFrame.
val chainWith2Friends2 = chain4.where(condition >= 2)
display(chainWith2Friends2)
chain4
res22: org.apache.spark.sql.DataFrame = [a: struct<id: string, name: string ... 1 more field>, ab: struct<src: string, dst: string ... 1 more field> ... 5 more fields]
chain4.printSchema
root
 |-- a: struct (nullable = false)
 |    |-- id: string (nullable = true)
 |    |-- name: string (nullable = true)
 |    |-- age: integer (nullable = false)
 |-- ab: struct (nullable = false)
 |    |-- src: string (nullable = true)
 |    |-- dst: string (nullable = true)
 |    |-- relationship: string (nullable = true)
 |-- b: struct (nullable = false)
 |    |-- id: string (nullable = true)
 |    |-- name: string (nullable = true)
 |    |-- age: integer (nullable = false)
 |-- bc: struct (nullable = false)
 |    |-- src: string (nullable = true)
 |    |-- dst: string (nullable = true)
 |    |-- relationship: string (nullable = true)
 |-- c: struct (nullable = false)
 |    |-- id: string (nullable = true)
 |    |-- name: string (nullable = true)
 |    |-- age: integer (nullable = false)
 |-- cd: struct (nullable = false)
 |    |-- src: string (nullable = true)
 |    |-- dst: string (nullable = true)
 |    |-- relationship: string (nullable = true)
 |-- d: struct (nullable = false)
 |    |-- id: string (nullable = true)
 |    |-- name: string (nullable = true)
 |    |-- age: integer (nullable = false)

An idea -- a diatribe into an AI security product.

Can you think of a way to use stateful queries in social media networks to find perpetrators of hate-speech online who are possibly worthy of an investigation by domain experts, say in the intelligence or security domain, for potential prosecution on charges of having incited another person to cause physical violence... This is a real problem today as Swedish law effectively prohibits certain forms of online hate-speech.

An idea for a product that can be used by Swedish security agencies?

See https://näthatsgranskaren.se/ for details of a non-profit in Sweden doing such operaitons mostly manually as of early 2020.

Subgraphs

Subgraphs are built by filtering a subset of edges and vertices. For example, the following subgraph only contains people who are friends and who are more than 30 years old.

// Select subgraph of users older than 30, and edges of type "friend"
val v2 = g.vertices.filter("age > 30")
val e2 = g.edges.filter("relationship = 'friend'")
val g2 = GraphFrame(v2, e2)
v2: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [id: string, name: string ... 1 more field]
e2: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [src: string, dst: string ... 1 more field]
g2: org.graphframes.GraphFrame = GraphFrame(v:[id: string, name: string ... 1 more field], e:[src: string, dst: string ... 1 more field])
display(g2.vertices)
id name age
a Alice 34.0
b Bob 36.0
e Esther 32.0
f Fanny 36.0
g Gabby 60.0
display(g2.edges)
src dst relationship
a b friend
e d friend
d a friend
a e friend
d3.graphs.force( // let us see g2 now in one cell
  height = 500,
  width = 500,
  clicks = g2.edges.select($"src", $"dst".as("dest"), lit(1L).as("count")).as[d3.Edge])

Complex triplet filters

The following example shows how to select a subgraph based upon triplet filters which operate on:

  • an edge and
  • its src and
  • dst vertices.

This example could be extended to go beyond triplets by using more complex motifs.

// Select subgraph based on edges "e" of type "follow"
// pointing from a younger user "a" to an older user "b".
val paths = g.find("(a)-[e]->(b)")
  .filter("e.relationship = 'follow'")
  .filter("a.age < b.age")
// "paths" contains vertex info. Extract the edges.
val e2 = paths.select("e.src", "e.dst", "e.relationship")
// In Spark 1.5+, the user may simplify this call:
//  val e2 = paths.select("e.*")

// Construct the subgraph
val g2 = GraphFrame(g.vertices, e2)
paths: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [a: struct<id: string, name: string ... 1 more field>, e: struct<src: string, dst: string ... 1 more field> ... 1 more field]
e2: org.apache.spark.sql.DataFrame = [src: string, dst: string ... 1 more field]
g2: org.graphframes.GraphFrame = GraphFrame(v:[id: string, name: string ... 1 more field], e:[src: string, dst: string ... 1 more field])
display(g2.vertices)
id name age
a Alice 34.0
b Bob 36.0
c Charlie 30.0
d David 29.0
e Esther 32.0
f Fanny 36.0
g Gabby 60.0
display(g2.edges)
src dst relationship
c b follow
e f follow

Standard graph algorithms in GraphX conveniently via GraphFrames

GraphFrames comes with a number of standard graph algorithms built in:

  • Breadth-first search (BFS)
  • Connected components
  • Strongly connected components
  • Label Propagation Algorithm (LPA)
  • PageRank
  • Shortest paths
  • Triangle count

Read

https://graphframes.github.io/graphframes/docs/_site/user-guide.html

Search from "Esther" for users of age < 32.

// Search from "Esther" for users of age <= 32.
val paths: DataFrame = g.bfs.fromExpr("name = 'Esther'").toExpr("age < 32").run()
display(paths)
val paths: DataFrame = g.bfs.fromExpr("name = 'Esther' OR name = 'Bob'").toExpr("age < 32").run()
display(paths)

The search may also be limited by edge filters and maximum path lengths.

val filteredPaths = g.bfs.fromExpr("name = 'Esther'").toExpr("age < 32")
  .edgeFilter("relationship != 'friend'")
  .maxPathLength(3)
  .run()
display(filteredPaths)

Connected components

Compute the connected component membership of each vertex and return a graph with each vertex assigned a component ID.

READ https://graphframes.github.io/graphframes/docs/_site/user-guide.html#connected-components.

From https://graphframes.github.io/graphframes/docs/_site/user-guide.html#connected-components:-

NOTE: With GraphFrames 0.3.0 and later releases, the default Connected Components algorithm requires setting a Spark checkpoint directory. Users can revert to the old algorithm using .setAlgorithm("graphx").

Recall the following quote from Chapter 5 on Effective Transformations of the High Performance Spark Book why one needs to check-point to keep the RDD lineage DAGs from growing too large.

Types of Reuse: Cache, Persist, Checkpoint, Shuffle Files If you decide that you need to reuse your RDD, Spark provides a multitude of options for how to store the RDD. Thus it is important to understand when to use the various types of persistence.There are three primary operations that you can use to store your RDD: cache, persist, and checkpoint. In general, caching (equivalent to persisting with the in-memory storage) and persisting are most useful to avoid recomputation during one Spark job or to break RDDs with long lineages, since they keep an RDD on the executors during a Spark job. Checkpointing is most useful to prevent failures and a high cost of recomputation by saving intermediate results. Like persisting, checkpointing helps avoid computation, thus minimizing the cost of failure, and avoids recomputation by breaking the lineage graph.

sc.setCheckpointDir("/_checkpoint") // just a directory in distributed file system
val result = g.connectedComponents.run() 
display(result)
id name age component
a Alice 34.0 4.12316860416e11
b Bob 36.0 4.12316860416e11
c Charlie 30.0 4.12316860416e11
d David 29.0 4.12316860416e11
e Esther 32.0 4.12316860416e11
f Fanny 36.0 4.12316860416e11
g Gabby 60.0 1.46028888064e11

Fun Exercise: Try to modify the d3.graph function to allow a visualisation of a given Sequence of component ids in the above result.

Strongly connected components

Compute the strongly connected component (SCC) of each vertex and return a graph with each vertex assigned to the SCC containing that vertex.

READ https://graphframes.github.io/graphframes/docs/_site/user-guide.html#strongly-connected-components.

val result = g.stronglyConnectedComponents.maxIter(10).run()
display(result.orderBy("component"))
id name age component
g Gabby 60.0 1.46028888064e11
f Fanny 36.0 4.12316860416e11
a Alice 34.0 6.70014898176e11
e Esther 32.0 6.70014898176e11
d David 29.0 6.70014898176e11
b Bob 36.0 1.047972020224e12
c Charlie 30.0 1.047972020224e12

Label propagation

Run static Label Propagation Algorithm for detecting communities in networks.

Each node in the network is initially assigned to its own community. At every superstep, nodes send their community affiliation to all neighbors and update their state to the mode community affiliation of incoming messages.

LPA is a standard community detection algorithm for graphs. It is very inexpensive computationally, although

  • (1) convergence is not guaranteed and
  • (2) one can end up with trivial solutions (all nodes are identified into a single community).

READ: https://graphframes.github.io/graphframes/docs/_site/user-guide.html#label-propagation-algorithm-lpa.

val result = g.labelPropagation.maxIter(5).run()
display(result.orderBy("label"))
id name age label
g Gabby 60.0 1.46028888064e11
b Bob 36.0 1.047972020224e12
e Esther 32.0 1.382979469312e12
a Alice 34.0 1.382979469312e12
c Charlie 30.0 1.382979469312e12
f Fanny 36.0 1.46028888064e12
d David 29.0 1.46028888064e12

PageRank

Identify important vertices in a graph based on connections.

READ: https://graphframes.github.io/graphframes/docs/_site/user-guide.html#pagerank.

// Run PageRank until convergence to tolerance "tol".
val results = g.pageRank.resetProbability(0.15).tol(0.01).run()
display(results.vertices)
id name age pagerank
b Bob 36.0 2.655507832863289
e Esther 32.0 0.37085233187676075
a Alice 34.0 0.44910633706538744
f Fanny 36.0 0.3283606792049851
g Gabby 60.0 0.1799821386239711
d David 29.0 0.3283606792049851
c Charlie 30.0 2.6878300011606218
display(results.edges)
src dst relationship weight
f c follow 1.0
e f follow 0.5
e d friend 0.5
d a friend 1.0
c b follow 1.0
b c follow 1.0
a e friend 0.5
a b friend 0.5
// Run PageRank for a fixed number of iterations.
val results2 = g.pageRank.resetProbability(0.15).maxIter(10).run()
display(results2.vertices)
id name age pagerank
b Bob 36.0 2.7025217677349773
e Esther 32.0 0.3613490987992571
a Alice 34.0 0.4485115093698443
f Fanny 36.0 0.32504910549694244
g Gabby 60.0 0.17073170731707318
d David 29.0 0.32504910549694244
c Charlie 30.0 2.6667877057849627
// Run PageRank personalized for vertex "a"
val results3 = g.pageRank.resetProbability(0.15).maxIter(10).sourceId("a").run()
display(results3.vertices)
id name age pagerank
b Bob 36.0 0.3366143039702568
e Esther 32.0 7.657840357273027e-2
a Alice 34.0 0.17710831642683564
f Fanny 36.0 3.189213697274781e-2
g Gabby 60.0 0.0
d David 29.0 3.189213697274781e-2
c Charlie 30.0 0.3459147020846817

Shortest paths

Computes shortest paths to the given set of landmark vertices, where landmarks are specified by vertex ID.

READ https://graphframes.github.io/graphframes/docs/_site/user-guide.html#shortest-paths.

val paths = g.shortestPaths.landmarks(Seq("a", "d")).run()
display(paths)
g.edges.show()
+---+---+------------+
|src|dst|relationship|
+---+---+------------+
|  a|  b|      friend|
|  b|  c|      follow|
|  c|  b|      follow|
|  f|  c|      follow|
|  e|  f|      follow|
|  e|  d|      friend|
|  d|  a|      friend|
|  a|  e|      friend|
+---+---+------------+

Triangle count

Computes the number of triangles passing through each vertex.

val results = g.triangleCount.run()
display(results)
count id name age
1.0 a Alice 34.0
0.0 b Bob 36.0
0.0 c Charlie 30.0
1.0 d David 29.0
1.0 e Esther 32.0
0.0 f Fanny 36.0
0.0 g Gabby 60.0

YouTry

Read about https://graphframes.github.io/graphframes/docs/_site/user-guide.html#message-passing-via-aggregatemessages

and undestand how the below code snippet shows how to use aggregateMessages to compute the sum of the ages of adjacent users.

import org.graphframes.{examples,GraphFrame}
import org.graphframes.lib.AggregateMessages
val g: GraphFrame = examples.Graphs.friends  // get example graph

// We will use AggregateMessages utilities later, so name it "AM" for short.
val AM = AggregateMessages

// For each user, sum the ages of the adjacent users.
val msgToSrc = AM.dst("age")
val msgToDst = AM.src("age")
val agg = { g.aggregateMessages
  .sendToSrc(msgToSrc)  // send destination user's age to source
  .sendToDst(msgToDst)  // send source user's age to destination
  .agg(sum(AM.msg).as("summedAges")) } // sum up ages, stored in AM.msg column
agg.show()
+---+----------+
| id|summedAges|
+---+----------+
|  a|        97|
|  c|       108|
|  e|        99|
|  d|        66|
|  b|        94|
|  f|        62|
+---+----------+

import org.graphframes.{examples, GraphFrame}
import org.graphframes.lib.AggregateMessages
g: org.graphframes.GraphFrame = GraphFrame(v:[id: string, name: string ... 1 more field], e:[src: string, dst: string ... 1 more field])
AM: org.graphframes.lib.AggregateMessages.type = org.graphframes.lib.AggregateMessages$@706833c8
msgToSrc: org.apache.spark.sql.Column = dst[age]
msgToDst: org.apache.spark.sql.Column = src[age]
agg: org.apache.spark.sql.DataFrame = [id: string, summedAges: bigint]

There is a lot more that can be done with aggregate messaging - let's get into belief propogation algorithm for a more complex example!

Belief propogation is a powerful computational framework for Graphical Models.

as

This provides a template for building customized BP algorithms for different types of graphical models.

Project Idea

Understand parallel belief propagation using colored fields in the Scala code linked above and also pasted below in one cell (for you to modify if you want to do it in a databricks or jupyter or zeppelin notebook) unless you want to fork and extend the github repo directly with your own example.

Then use it with necessary adaptations to be able to model your favorite interacting particle system. Don't just redo the Ising model done there!

This can be used to gain intuition for various real-world scenarios, including the mathematics in your head:

  • Make a graph for contact network of a set of hosts
  • A simple model of COVID spreading in an SI or SIS or SIR or other epidemic models
    • this can be abstract and simply show your skills in programming, say create a random network
    • or be more explicit with some assumptions about the contact process (population sampled, in one or two cities, with some assumptions on contacts during transportation, school, work, etc)
    • show that you have a fully scalable simulation model that can theoretically scale to billions of hosts

The project does not have to be a recommendation to Swedish authorities! Just a start in the right direction, for instance.

Some readings that can help here include the following and references therein:

  • The Transmission Process: A Combinatorial Stochastic Process for the Evolution of Transmission Trees over Networks, Raazesh Sainudiin and David Welch, Journal of Theoretical Biology, Volume 410, Pages 137–170, 10.1016/j.jtbi.2016.07.038, 2016.

Other Project Ideas

  • try to do a scalable inference algorithm for one of the graphical models that you already know...
  • make a large simulaiton of your favourite Finite Markov Information Exchange (FMIE) process defined by Aldous (see reference in the above linked paper)
  • anything else that fancies you or your research orientation/interests and can benefit from adapting the template for the parallel belief propagation algorithm here.

If you want to do this project in databricks (or other) notebook then start by modifying the following code from the example and making it run... Then adapt... start in small steps... make a team with fellow students with complementary skills...

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *    http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.graphframes.examples

import org.apache.spark.{SparkConf, SparkContext}
import org.apache.spark.graphx.{Graph, VertexRDD, Edge => GXEdge}
import org.apache.spark.sql.{Column, Row, SparkSession, SQLContext}
import org.apache.spark.sql.functions.{col, lit, sum, udf, when}

import org.graphframes.GraphFrame
import org.graphframes.examples.Graphs.gridIsingModel
import org.graphframes.lib.AggregateMessages


/**
 * Example code for Belief Propagation (BP)
 *
 * This provides a template for building customized BP algorithms for different types of
 * graphical models.
 *
 * This example:
 *  - Ising model on a grid
 *  - Parallel Belief Propagation using colored fields
 *
 * Ising models are probabilistic graphical models over binary variables x,,i,,.
 * Each binary variable x,,i,, corresponds to one vertex, and it may take values -1 or +1.
 * The probability distribution P(X) (over all x,,i,,) is parameterized by vertex factors a,,i,,
 * and edge factors b,,ij,,:
 * {{{
 *  P(X) = (1/Z) * exp[ \sum_i a_i x_i + \sum_{ij} b_{ij} x_i x_j ]
 * }}}
 * where Z is the normalization constant (partition function).
 * See [[https://en.wikipedia.org/wiki/Ising_model Wikipedia]] for more information on Ising models.
 *
 * Belief Propagation (BP) provides marginal probabilities of the values of the variables x,,i,,,
 * i.e., P(x,,i,,) for each i.  This allows a user to understand likely values of variables.
 * See [[https://en.wikipedia.org/wiki/Belief_propagation Wikipedia]] for more information on BP.
 *
 * We use a batch synchronous BP algorithm, where batches of vertices are updated synchronously.
 * We follow the mean field update algorithm in Slide 13 of the
 * [[http://www.eecs.berkeley.edu/~wainwrig/Talks/A_GraphModel_Tutorial  talk slides]] from:
 *  Wainwright. "Graphical models, message-passing algorithms, and convex optimization."
 *
 * The batches are chosen according to a coloring.  For background on graph colorings for inference,
 * see for example:
 *  Gonzalez et al. "Parallel Gibbs Sampling: From Colored Fields to Thin Junction Trees."
 *  AISTATS, 2011.
 *
 * The BP algorithm works by:
 *  - Coloring the graph by assigning a color to each vertex such that no neighboring vertices
 *    share the same color.
 *  - In each step of BP, update all vertices of a single color.  Alternate colors.
 */
object BeliefPropagation {

  def main(args: Array[String]): Unit = {
    val spark = SparkSession
      .builder()
      .appName("BeliefPropagation example")
      .getOrCreate()

    val sql = spark.sqlContext

    // Create graphical model g of size 3 x 3.
    val g = gridIsingModel(sql, 3)

    println("Original Ising model:")
    g.vertices.show()
    g.edges.show()

    // Run BP for 5 iterations.
    val numIter = 5
    val results = runBPwithGraphX(g, numIter)

    // Display beliefs.
    val beliefs = results.vertices.select("id", "belief")
    println(s"Done with BP. Final beliefs after $numIter iterations:")
    beliefs.show()

    spark.stop()
  }

  /**
   * Given a GraphFrame, choose colors for each vertex.  No neighboring vertices will share the
   * same color.  The number of colors is minimized.
   *
   * This is written specifically for grid graphs. For non-grid graphs, it should be generalized,
   * such as by using a greedy coloring scheme.
   *
   * @param g  Grid graph generated by [[org.graphframes.examples.Graphs.gridIsingModel()]]
   * @return  Same graph, but with a new vertex column "color" of type Int (0 or 1)
   */
  private def colorGraph(g: GraphFrame): GraphFrame = {
    val colorUDF = udf { (i: Int, j: Int) => (i + j) % 2 }
    val v = g.vertices.withColumn("color", colorUDF(col("i"), col("j")))
    GraphFrame(v, g.edges)
  }

  /**
   * Run Belief Propagation.
   *
   * This implementation of BP shows how to use GraphX's aggregateMessages method.
   * It is simple to convert to and from GraphX format.  This method does the following:
   *  - Color GraphFrame vertices for BP scheduling.
   *  - Convert GraphFrame to GraphX format.
   *  - Run BP using GraphX's aggregateMessages API.
   *  - Augment the original GraphFrame with the BP results (vertex beliefs).
   *
   * @param g  Graphical model created by `org.graphframes.examples.Graphs.gridIsingModel()`
   * @param numIter  Number of iterations of BP to run.  One iteration includes updating each
   *                 vertex's belief once.
   * @return  Same graphical model, but with [[GraphFrame.vertices]] augmented with a new column
   *          "belief" containing P(x,,i,, = +1), the marginal probability of vertex i taking
   *          value +1 instead of -1.
   */
  def runBPwithGraphX(g: GraphFrame, numIter: Int): GraphFrame = {
    // Choose colors for vertices for BP scheduling.
    val colorG = colorGraph(g)
    val numColors: Int = colorG.vertices.select("color").distinct.count().toInt

    // Convert GraphFrame to GraphX, and initialize beliefs.
    val gx0 = colorG.toGraphX
    // Schema maps for extracting attributes
    val vColsMap = colorG.vertexColumnMap
    val eColsMap = colorG.edgeColumnMap
    // Convert vertex attributes to nice case classes.
    val gx1: Graph[VertexAttr, Row] = gx0.mapVertices { case (_, attr) =>
      // Initialize belief at 0.0
      VertexAttr(attr.getDouble(vColsMap("a")), 0.0, attr.getInt(vColsMap("color")))
    }
    // Convert edge attributes to nice case classes.
    val extractEdgeAttr: (GXEdge[Row] => EdgeAttr) = { e =>
      EdgeAttr(e.attr.getDouble(eColsMap("b")))
    }
    var gx: Graph[VertexAttr, EdgeAttr] = gx1.mapEdges(extractEdgeAttr)

    // Run BP for numIter iterations.
    for (iter <- Range(0, numIter)) {
      // For each color, have that color receive messages from neighbors.
      for (color <- Range(0, numColors)) {
        // Send messages to vertices of the current color.
        val msgs: VertexRDD[Double] = gx.aggregateMessages(
          ctx =>
            // Can send to source or destination since edges are treated as undirected.
            if (ctx.dstAttr.color == color) {
              val msg = ctx.attr.b * ctx.srcAttr.belief
              // Only send message if non-zero.
              if (msg != 0) ctx.sendToDst(msg)
            } else if (ctx.srcAttr.color == color) {
              val msg = ctx.attr.b * ctx.dstAttr.belief
              // Only send message if non-zero.
              if (msg != 0) ctx.sendToSrc(msg)
            },
          _ + _)
        // Receive messages, and update beliefs for vertices of the current color.
        gx = gx.outerJoinVertices(msgs) {
          case (vID, vAttr, optMsg) =>
            if (vAttr.color == color) {
              val x = vAttr.a + optMsg.getOrElse(0.0)
              val newBelief = math.exp(-log1pExp(-x))
              VertexAttr(vAttr.a, newBelief, color)
            } else {
              vAttr
            }
        }
      }
    }

    // Convert back to GraphFrame with a new column "belief" for vertices DataFrame.
    val gxFinal: Graph[Double, Unit] = gx.mapVertices((_, attr) => attr.belief).mapEdges(_ => ())
    GraphFrame.fromGraphX(colorG, gxFinal, vertexNames = Seq("belief"))
  }

  case class VertexAttr(a: Double, belief: Double, color: Int)

  case class EdgeAttr(b: Double)

  /**
   * Run Belief Propagation.
   *
   * This implementation of BP shows how to use GraphFrame's aggregateMessages method.
   *  - Color GraphFrame vertices for BP scheduling.
   *  - Run BP using GraphFrame's aggregateMessages API.
   *  - Augment the original GraphFrame with the BP results (vertex beliefs).
   *
   * @param g  Graphical model created by `org.graphframes.examples.Graphs.gridIsingModel()`
   * @param numIter  Number of iterations of BP to run.  One iteration includes updating each
   *                 vertex's belief once.
   * @return  Same graphical model, but with [[GraphFrame.vertices]] augmented with a new column
   *          "belief" containing P(x,,i,, = +1), the marginal probability of vertex i taking
   *          value +1 instead of -1.
   */
  def runBPwithGraphFrames(g: GraphFrame, numIter: Int): GraphFrame = {
    // Choose colors for vertices for BP scheduling.
    val colorG = colorGraph(g)
    val numColors: Int = colorG.vertices.select("color").distinct.count().toInt

    // TODO: Handle vertices without any edges.

    // Initialize vertex beliefs at 0.0.
    var gx = GraphFrame(colorG.vertices.withColumn("belief", lit(0.0)), colorG.edges)

    // Run BP for numIter iterations.
    for (iter <- Range(0, numIter)) {
      // For each color, have that color receive messages from neighbors.
      for (color <- Range(0, numColors)) {
        // Define "AM" for shorthand for referring to the src, dst, edge, and msg fields.
        // (See usage below.)
        val AM = AggregateMessages
        // Send messages to vertices of the current color.
        // We may send to source or destination since edges are treated as undirected.
        val msgForSrc: Column = when(AM.src("color") === color, AM.edge("b") * AM.dst("belief"))
        val msgForDst: Column = when(AM.dst("color") === color, AM.edge("b") * AM.src("belief"))
        val logistic = udf { (x: Double) => math.exp(-log1pExp(-x)) }
        val aggregates = gx.aggregateMessages
          .sendToSrc(msgForSrc)
          .sendToDst(msgForDst)
          .agg(sum(AM.msg).as("aggMess"))
        val v = gx.vertices
        // Receive messages, and update beliefs for vertices of the current color.
        val newBeliefCol = when(v("color") === color && aggregates("aggMess").isNotNull,
          logistic(aggregates("aggMess") + v("a")))
          .otherwise(v("belief"))  // keep old beliefs for other colors
        val newVertices = v
          .join(aggregates, v("id") === aggregates("id"), "left_outer")  // join messages, vertices
          .drop(aggregates("id"))  // drop duplicate ID column (from outer join)
          .withColumn("newBelief", newBeliefCol)  // compute new beliefs
          .drop("aggMess")  // drop messages
          .drop("belief")  // drop old beliefs
          .withColumnRenamed("newBelief", "belief")
        // Cache new vertices using workaround for SPARK-13346
        val cachedNewVertices = AM.getCachedDataFrame(newVertices)
        gx = GraphFrame(cachedNewVertices, gx.edges)
      }
    }

    // Drop the "color" column from vertices
    GraphFrame(gx.vertices.drop("color"), gx.edges)
  }

  /** More numerically stable `log(1 + exp(x))` */
  private def log1pExp(x: Double): Double = {
    if (x > 0) {
      x + math.log1p(math.exp(-x))
    } else {
      math.log1p(math.exp(x))
    }
  }
}

ScaDaMaLe Course site and book

This is a scala version of the python notebook in the following talk:

Homework:

See https://www.brighttalk.com/webcast/12891/199003 (you need to subscribe freely to Bright Talk first). Then go through this scala version of the notebook from the talk.

On-Time Flight Performance with GraphFrames for Apache Spark

This notebook provides an analysis of On-Time Flight Performance and Departure Delays data using GraphFrames for Apache Spark.

Source Data:

References:

Preparation

Extract the Airports and Departure Delays information from S3 / DBFS

// Set File Paths
val tripdelaysFilePath = "/datasets/sds/flights/departuredelays.csv"
val airportsnaFilePath = "/datasets/sds/flights/airport-codes-na.txt"
tripdelaysFilePath: String = /datasets/sds/flights/departuredelays.csv
airportsnaFilePath: String = /datasets/sds/flights/airport-codes-na.txt
// Obtain airports dataset
// Note that "spark-csv" package is built-in datasource in Spark 2.0
val airportsna = sqlContext.read.format("com.databricks.spark.csv").
  option("header", "true").
  option("inferschema", "true").
  option("delimiter", "\t").
  load(airportsnaFilePath)

airportsna.createOrReplaceTempView("airports_na")

// Obtain departure Delays data
val departureDelays = sqlContext.read.format("com.databricks.spark.csv").option("header", "true").load(tripdelaysFilePath)
departureDelays.createOrReplaceTempView("departureDelays")
departureDelays.cache()

// Available IATA (International Air Transport Association) codes from the departuredelays sample dataset
val tripIATA = sqlContext.sql("select distinct iata from (select distinct origin as iata from departureDelays union all select distinct destination as iata from departureDelays) a")
tripIATA.createOrReplaceTempView("tripIATA")

// Only include airports with atleast one trip from the departureDelays dataset
val airports = sqlContext.sql("select f.IATA, f.City, f.State, f.Country from airports_na f join tripIATA t on t.IATA = f.IATA")
airports.createOrReplaceTempView("airports")
airports.cache()
airportsna: org.apache.spark.sql.DataFrame = [City: string, State: string ... 2 more fields]
departureDelays: org.apache.spark.sql.DataFrame = [date: string, delay: string ... 3 more fields]
tripIATA: org.apache.spark.sql.DataFrame = [iata: string]
airports: org.apache.spark.sql.DataFrame = [IATA: string, City: string ... 2 more fields]
res0: airports.type = [IATA: string, City: string ... 2 more fields]
// Build `departureDelays_geo` DataFrame
// Obtain key attributes such as Date of flight, delays, distance, and airport information (Origin, Destination)  
val departureDelays_geo = sqlContext.sql("select cast(f.date as int) as tripid, cast(concat(concat(concat(concat(concat(concat('2014-', concat(concat(substr(cast(f.date as string), 1, 2), '-')), substr(cast(f.date as string), 3, 2)), ' '), substr(cast(f.date as string), 5, 2)), ':'), substr(cast(f.date as string), 7, 2)), ':00') as timestamp) as `localdate`, cast(f.delay as int), cast(f.distance as int), f.origin as src, f.destination as dst, o.city as city_src, d.city as city_dst, o.state as state_src, d.state as state_dst from departuredelays f join airports o on o.iata = f.origin join airports d on d.iata = f.destination") 

// RegisterTempTable
departureDelays_geo.createOrReplaceTempView("departureDelays_geo")

// Cache and Count
departureDelays_geo.cache()
departureDelays_geo.count()
departureDelays_geo: org.apache.spark.sql.DataFrame = [tripid: int, localdate: timestamp ... 8 more fields]
res2: Long = 1361141
display(departureDelays_geo)
tripid localdate delay distance src dst city_src city_dst state_src state_dst
1011111.0 2014-01-01T11:11:00.000+0000 -5.0 221.0 MSP INL Minneapolis International Falls MN MN
1021111.0 2014-01-02T11:11:00.000+0000 7.0 221.0 MSP INL Minneapolis International Falls MN MN
1031111.0 2014-01-03T11:11:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
1041925.0 2014-01-04T19:25:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
1061115.0 2014-01-06T11:15:00.000+0000 33.0 221.0 MSP INL Minneapolis International Falls MN MN
1071115.0 2014-01-07T11:15:00.000+0000 23.0 221.0 MSP INL Minneapolis International Falls MN MN
1081115.0 2014-01-08T11:15:00.000+0000 -9.0 221.0 MSP INL Minneapolis International Falls MN MN
1091115.0 2014-01-09T11:15:00.000+0000 11.0 221.0 MSP INL Minneapolis International Falls MN MN
1101115.0 2014-01-10T11:15:00.000+0000 -3.0 221.0 MSP INL Minneapolis International Falls MN MN
1112015.0 2014-01-11T20:15:00.000+0000 -7.0 221.0 MSP INL Minneapolis International Falls MN MN
1121925.0 2014-01-12T19:25:00.000+0000 -5.0 221.0 MSP INL Minneapolis International Falls MN MN
1131115.0 2014-01-13T11:15:00.000+0000 -3.0 221.0 MSP INL Minneapolis International Falls MN MN
1141115.0 2014-01-14T11:15:00.000+0000 -6.0 221.0 MSP INL Minneapolis International Falls MN MN
1151115.0 2014-01-15T11:15:00.000+0000 -7.0 221.0 MSP INL Minneapolis International Falls MN MN
1161115.0 2014-01-16T11:15:00.000+0000 -3.0 221.0 MSP INL Minneapolis International Falls MN MN
1171115.0 2014-01-17T11:15:00.000+0000 4.0 221.0 MSP INL Minneapolis International Falls MN MN
1182015.0 2014-01-18T20:15:00.000+0000 -5.0 221.0 MSP INL Minneapolis International Falls MN MN
1191925.0 2014-01-19T19:25:00.000+0000 -7.0 221.0 MSP INL Minneapolis International Falls MN MN
1201115.0 2014-01-20T11:15:00.000+0000 -6.0 221.0 MSP INL Minneapolis International Falls MN MN
1211115.0 2014-01-21T11:15:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
1221115.0 2014-01-22T11:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
1231115.0 2014-01-23T11:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
1241115.0 2014-01-24T11:15:00.000+0000 -3.0 221.0 MSP INL Minneapolis International Falls MN MN
1252015.0 2014-01-25T20:15:00.000+0000 -12.0 221.0 MSP INL Minneapolis International Falls MN MN
1261925.0 2014-01-26T19:25:00.000+0000 -5.0 221.0 MSP INL Minneapolis International Falls MN MN
1271115.0 2014-01-27T11:15:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
1281115.0 2014-01-28T11:15:00.000+0000 -8.0 221.0 MSP INL Minneapolis International Falls MN MN
1291115.0 2014-01-29T11:15:00.000+0000 -2.0 221.0 MSP INL Minneapolis International Falls MN MN
1301115.0 2014-01-30T11:15:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
1311115.0 2014-01-31T11:15:00.000+0000 -3.0 221.0 MSP INL Minneapolis International Falls MN MN
2012015.0 2014-02-01T20:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
2022015.0 2014-02-02T20:15:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
2031115.0 2014-02-03T11:15:00.000+0000 -7.0 221.0 MSP INL Minneapolis International Falls MN MN
2041115.0 2014-02-04T11:15:00.000+0000 -6.0 221.0 MSP INL Minneapolis International Falls MN MN
2051115.0 2014-02-05T11:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
2061115.0 2014-02-06T11:15:00.000+0000 -2.0 221.0 MSP INL Minneapolis International Falls MN MN
2071115.0 2014-02-07T11:15:00.000+0000 -15.0 221.0 MSP INL Minneapolis International Falls MN MN
2082015.0 2014-02-08T20:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
2091925.0 2014-02-09T19:25:00.000+0000 1.0 221.0 MSP INL Minneapolis International Falls MN MN
2101115.0 2014-02-10T11:15:00.000+0000 -3.0 221.0 MSP INL Minneapolis International Falls MN MN
2111115.0 2014-02-11T11:15:00.000+0000 -7.0 221.0 MSP INL Minneapolis International Falls MN MN
2121115.0 2014-02-12T11:15:00.000+0000 -2.0 221.0 MSP INL Minneapolis International Falls MN MN
2131115.0 2014-02-13T11:15:00.000+0000 -3.0 221.0 MSP INL Minneapolis International Falls MN MN
2141115.0 2014-02-14T11:15:00.000+0000 -11.0 221.0 MSP INL Minneapolis International Falls MN MN
2152015.0 2014-02-15T20:15:00.000+0000 16.0 221.0 MSP INL Minneapolis International Falls MN MN
2161925.0 2014-02-16T19:25:00.000+0000 169.0 221.0 MSP INL Minneapolis International Falls MN MN
2171115.0 2014-02-17T11:15:00.000+0000 27.0 221.0 MSP INL Minneapolis International Falls MN MN
2181115.0 2014-02-18T11:15:00.000+0000 96.0 221.0 MSP INL Minneapolis International Falls MN MN
2191115.0 2014-02-19T11:15:00.000+0000 -9.0 221.0 MSP INL Minneapolis International Falls MN MN
2201115.0 2014-02-20T11:15:00.000+0000 -6.0 221.0 MSP INL Minneapolis International Falls MN MN
2211115.0 2014-02-21T11:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
2222015.0 2014-02-22T20:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
2231925.0 2014-02-23T19:25:00.000+0000 -3.0 221.0 MSP INL Minneapolis International Falls MN MN
2241115.0 2014-02-24T11:15:00.000+0000 -2.0 221.0 MSP INL Minneapolis International Falls MN MN
2251115.0 2014-02-25T11:15:00.000+0000 -6.0 221.0 MSP INL Minneapolis International Falls MN MN
2261115.0 2014-02-26T11:15:00.000+0000 -8.0 221.0 MSP INL Minneapolis International Falls MN MN
2271115.0 2014-02-27T11:15:00.000+0000 -8.0 221.0 MSP INL Minneapolis International Falls MN MN
2281115.0 2014-02-28T11:15:00.000+0000 5.0 221.0 MSP INL Minneapolis International Falls MN MN
3012015.0 2014-03-01T20:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
3022000.0 2014-03-02T20:00:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
3031115.0 2014-03-03T11:15:00.000+0000 17.0 221.0 MSP INL Minneapolis International Falls MN MN
3041115.0 2014-03-04T11:15:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
3051115.0 2014-03-05T11:15:00.000+0000 -7.0 221.0 MSP INL Minneapolis International Falls MN MN
3061115.0 2014-03-06T11:15:00.000+0000 -8.0 221.0 MSP INL Minneapolis International Falls MN MN
3071115.0 2014-03-07T11:15:00.000+0000 -10.0 221.0 MSP INL Minneapolis International Falls MN MN
3082000.0 2014-03-08T20:00:00.000+0000 -11.0 221.0 MSP INL Minneapolis International Falls MN MN
3092000.0 2014-03-09T20:00:00.000+0000 -9.0 221.0 MSP INL Minneapolis International Falls MN MN
3101115.0 2014-03-10T11:15:00.000+0000 -10.0 221.0 MSP INL Minneapolis International Falls MN MN
3111115.0 2014-03-11T11:15:00.000+0000 -8.0 221.0 MSP INL Minneapolis International Falls MN MN
3121115.0 2014-03-12T11:15:00.000+0000 -6.0 221.0 MSP INL Minneapolis International Falls MN MN
3131115.0 2014-03-13T11:15:00.000+0000 -8.0 221.0 MSP INL Minneapolis International Falls MN MN
3141115.0 2014-03-14T11:15:00.000+0000 -5.0 221.0 MSP INL Minneapolis International Falls MN MN
3152000.0 2014-03-15T20:00:00.000+0000 -11.0 221.0 MSP INL Minneapolis International Falls MN MN
3162000.0 2014-03-16T20:00:00.000+0000 -10.0 221.0 MSP INL Minneapolis International Falls MN MN
3171115.0 2014-03-17T11:15:00.000+0000 25.0 221.0 MSP INL Minneapolis International Falls MN MN
3181115.0 2014-03-18T11:15:00.000+0000 2.0 221.0 MSP INL Minneapolis International Falls MN MN
3191115.0 2014-03-19T11:15:00.000+0000 -5.0 221.0 MSP INL Minneapolis International Falls MN MN
3201115.0 2014-03-20T11:15:00.000+0000 -6.0 221.0 MSP INL Minneapolis International Falls MN MN
3211115.0 2014-03-21T11:15:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
3222000.0 2014-03-22T20:00:00.000+0000 -10.0 221.0 MSP INL Minneapolis International Falls MN MN
3232000.0 2014-03-23T20:00:00.000+0000 -9.0 221.0 MSP INL Minneapolis International Falls MN MN
3241115.0 2014-03-24T11:15:00.000+0000 -9.0 221.0 MSP INL Minneapolis International Falls MN MN
3251115.0 2014-03-25T11:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
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1270850.0 2014-01-27T08:50:00.000+0000 -2.0 409.0 BNA MSY Nashville New Orleans TN LA
1271735.0 2014-01-27T17:35:00.000+0000 10.0 409.0 BNA MSY Nashville New Orleans TN LA
1281240.0 2014-01-28T12:40:00.000+0000 0.0 409.0 BNA MSY Nashville New Orleans TN LA
1281455.0 2014-01-28T14:55:00.000+0000 0.0 409.0 BNA MSY Nashville New Orleans TN LA
1280850.0 2014-01-28T08:50:00.000+0000 0.0 409.0 BNA MSY Nashville New Orleans TN LA
1281735.0 2014-01-28T17:35:00.000+0000 0.0 409.0 BNA MSY Nashville New Orleans TN LA
1291240.0 2014-01-29T12:40:00.000+0000 13.0 409.0 BNA MSY Nashville New Orleans TN LA
1291455.0 2014-01-29T14:55:00.000+0000 -2.0 409.0 BNA MSY Nashville New Orleans TN LA
1290850.0 2014-01-29T08:50:00.000+0000 0.0 409.0 BNA MSY Nashville New Orleans TN LA
1291735.0 2014-01-29T17:35:00.000+0000 9.0 409.0 BNA MSY Nashville New Orleans TN LA
1301240.0 2014-01-30T12:40:00.000+0000 38.0 409.0 BNA MSY Nashville New Orleans TN LA
1301455.0 2014-01-30T14:55:00.000+0000 6.0 409.0 BNA MSY Nashville New Orleans TN LA
1300850.0 2014-01-30T08:50:00.000+0000 -1.0 409.0 BNA MSY Nashville New Orleans TN LA
1301735.0 2014-01-30T17:35:00.000+0000 57.0 409.0 BNA MSY Nashville New Orleans TN LA
1311240.0 2014-01-31T12:40:00.000+0000 31.0 409.0 BNA MSY Nashville New Orleans TN LA
1311455.0 2014-01-31T14:55:00.000+0000 22.0 409.0 BNA MSY Nashville New Orleans TN LA
1310850.0 2014-01-31T08:50:00.000+0000 -2.0 409.0 BNA MSY Nashville New Orleans TN LA
1311735.0 2014-01-31T17:35:00.000+0000 6.0 409.0 BNA MSY Nashville New Orleans TN LA
2011305.0 2014-02-01T13:05:00.000+0000 -1.0 409.0 BNA MSY Nashville New Orleans TN LA
2011805.0 2014-02-01T18:05:00.000+0000 -6.0 409.0 BNA MSY Nashville New Orleans TN LA
2010950.0 2014-02-01T09:50:00.000+0000 4.0 409.0 BNA MSY Nashville New Orleans TN LA
2021455.0 2014-02-02T14:55:00.000+0000 11.0 409.0 BNA MSY Nashville New Orleans TN LA
2021235.0 2014-02-02T12:35:00.000+0000 26.0 409.0 BNA MSY Nashville New Orleans TN LA
2021650.0 2014-02-02T16:50:00.000+0000 77.0 409.0 BNA MSY Nashville New Orleans TN LA
2031240.0 2014-02-03T12:40:00.000+0000 30.0 409.0 BNA MSY Nashville New Orleans TN LA
2031455.0 2014-02-03T14:55:00.000+0000 10.0 409.0 BNA MSY Nashville New Orleans TN LA
2030850.0 2014-02-03T08:50:00.000+0000 -1.0 409.0 BNA MSY Nashville New Orleans TN LA
2031735.0 2014-02-03T17:35:00.000+0000 -3.0 409.0 BNA MSY Nashville New Orleans TN LA
2041240.0 2014-02-04T12:40:00.000+0000 56.0 409.0 BNA MSY Nashville New Orleans TN LA
2041455.0 2014-02-04T14:55:00.000+0000 23.0 409.0 BNA MSY Nashville New Orleans TN LA
2040850.0 2014-02-04T08:50:00.000+0000 -1.0 409.0 BNA MSY Nashville New Orleans TN LA
2041735.0 2014-02-04T17:35:00.000+0000 3.0 409.0 BNA MSY Nashville New Orleans TN LA
2051240.0 2014-02-05T12:40:00.000+0000 33.0 409.0 BNA MSY Nashville New Orleans TN LA
2051455.0 2014-02-05T14:55:00.000+0000 14.0 409.0 BNA MSY Nashville New Orleans TN LA
2050850.0 2014-02-05T08:50:00.000+0000 19.0 409.0 BNA MSY Nashville New Orleans TN LA
2051735.0 2014-02-05T17:35:00.000+0000 26.0 409.0 BNA MSY Nashville New Orleans TN LA
2061240.0 2014-02-06T12:40:00.000+0000 43.0 409.0 BNA MSY Nashville New Orleans TN LA
2061455.0 2014-02-06T14:55:00.000+0000 -2.0 409.0 BNA MSY Nashville New Orleans TN LA
2060850.0 2014-02-06T08:50:00.000+0000 10.0 409.0 BNA MSY Nashville New Orleans TN LA
2061735.0 2014-02-06T17:35:00.000+0000 34.0 409.0 BNA MSY Nashville New Orleans TN LA
2071240.0 2014-02-07T12:40:00.000+0000 88.0 409.0 BNA MSY Nashville New Orleans TN LA
2071455.0 2014-02-07T14:55:00.000+0000 5.0 409.0 BNA MSY Nashville New Orleans TN LA
2070850.0 2014-02-07T08:50:00.000+0000 1.0 409.0 BNA MSY Nashville New Orleans TN LA
2071735.0 2014-02-07T17:35:00.000+0000 20.0 409.0 BNA MSY Nashville New Orleans TN LA
2081305.0 2014-02-08T13:05:00.000+0000 -6.0 409.0 BNA MSY Nashville New Orleans TN LA
2081805.0 2014-02-08T18:05:00.000+0000 0.0 409.0 BNA MSY Nashville New Orleans TN LA
2080950.0 2014-02-08T09:50:00.000+0000 -3.0 409.0 BNA MSY Nashville New Orleans TN LA
2091235.0 2014-02-09T12:35:00.000+0000 5.0 409.0 BNA MSY Nashville New Orleans TN LA
2091455.0 2014-02-09T14:55:00.000+0000 2.0 409.0 BNA MSY Nashville New Orleans TN LA
2091735.0 2014-02-09T17:35:00.000+0000 8.0 409.0 BNA MSY Nashville New Orleans TN LA
2101240.0 2014-02-10T12:40:00.000+0000 25.0 409.0 BNA MSY Nashville New Orleans TN LA
2101455.0 2014-02-10T14:55:00.000+0000 14.0 409.0 BNA MSY Nashville New Orleans TN LA
2100850.0 2014-02-10T08:50:00.000+0000 9.0 409.0 BNA MSY Nashville New Orleans TN LA
2101735.0 2014-02-10T17:35:00.000+0000 -2.0 409.0 BNA MSY Nashville New Orleans TN LA
2111240.0 2014-02-11T12:40:00.000+0000 145.0 409.0 BNA MSY Nashville New Orleans TN LA
2111455.0 2014-02-11T14:55:00.000+0000 -2.0 409.0 BNA MSY Nashville New Orleans TN LA
2110850.0 2014-02-11T08:50:00.000+0000 96.0 409.0 BNA MSY Nashville New Orleans TN LA
2111735.0 2014-02-11T17:35:00.000+0000 25.0 409.0 BNA MSY Nashville New Orleans TN LA
2121240.0 2014-02-12T12:40:00.000+0000 8.0 409.0 BNA MSY Nashville New Orleans TN LA
2121455.0 2014-02-12T14:55:00.000+0000 29.0 409.0 BNA MSY Nashville New Orleans TN LA
2120850.0 2014-02-12T08:50:00.000+0000 3.0 409.0 BNA MSY Nashville New Orleans TN LA
2121735.0 2014-02-12T17:35:00.000+0000 39.0 409.0 BNA MSY Nashville New Orleans TN LA
2131350.0 2014-02-13T13:50:00.000+0000 5.0 409.0 BNA MSY Nashville New Orleans TN LA
2131610.0 2014-02-13T16:10:00.000+0000 11.0 409.0 BNA MSY Nashville New Orleans TN LA
2130810.0 2014-02-13T08:10:00.000+0000 -4.0 409.0 BNA MSY Nashville New Orleans TN LA
2131800.0 2014-02-13T18:00:00.000+0000 9.0 409.0 BNA MSY Nashville New Orleans TN LA
2141610.0 2014-02-14T16:10:00.000+0000 37.0 409.0 BNA MSY Nashville New Orleans TN LA
2140810.0 2014-02-14T08:10:00.000+0000 13.0 409.0 BNA MSY Nashville New Orleans TN LA
2141350.0 2014-02-14T13:50:00.000+0000 46.0 409.0 BNA MSY Nashville New Orleans TN LA
2141800.0 2014-02-14T18:00:00.000+0000 21.0 409.0 BNA MSY Nashville New Orleans TN LA

Building the Graph

Now that we've imported our data, we're going to need to build our graph. To do so we're going to do two things. We are going to build the structure of the vertices (or nodes) and we're going to build the structure of the edges. What's awesome about GraphFrames is that this process is incredibly simple.

  • Rename IATA airport code to id in the Vertices Table
  • Start and End airports to src and dst for the Edges Table (flights)

These are required naming conventions for vertices and edges in GraphFrames.

WARNING: If the graphframes package, required in the cell below, is not installed, follow the instructions here.

// Note, ensure you have already installed the GraphFrames spack-package
import org.apache.spark.sql.functions._
import org.graphframes._

// Create Vertices (airports) and Edges (flights)
val tripVertices = airports.withColumnRenamed("IATA", "id").distinct()
val tripEdges = departureDelays_geo.select("tripid", "delay", "src", "dst", "city_dst", "state_dst")

// Cache Vertices and Edges
tripEdges.cache()
tripVertices.cache()
import org.apache.spark.sql.functions._
import org.graphframes._
tripVertices: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [id: string, City: string ... 2 more fields]
tripEdges: org.apache.spark.sql.DataFrame = [tripid: int, delay: int ... 4 more fields]
res5: tripVertices.type = [id: string, City: string ... 2 more fields]
// Vertices
// The vertices of our graph are the airports
display(tripVertices)
id City State Country
FAT Fresno CA USA
CMH Columbus OH USA
PHX Phoenix AZ USA
PAH Paducah KY USA
COS Colorado Springs CO USA
RNO Reno NV USA
MYR Myrtle Beach SC USA
VLD Valdosta GA USA
BPT Beaumont TX USA
CAE Columbia SC USA
PSC Pasco WA USA
SRQ Sarasota FL USA
LAX Los Angeles CA USA
DAY Dayton OH USA
AVP Wilkes-Barre PA USA
MFR Medford OR USA
JFK New York NY USA
BNA Nashville TN USA
CLT Charlotte NC USA
LAS Las Vegas NV USA
BDL Hartford CT USA
ILG Wilmington DE USA
ACT Waco TX USA
ATW Appleton WI USA
RHI Rhinelander WI USA
PWM Portland ME USA
SJT San Angelo TX USA
APN Alpena MI USA
GRB Green Bay WI USA
CAK Akron OH USA
LAN Lansing MI USA
FLL Fort Lauderdale FL USA
MSY New Orleans LA USA
SAT San Antonio TX USA
TPA Tampa FL USA
COD Cody WY USA
MOD Modesto CA USA
GTR Columbus MS USA
BTV Burlington VT USA
RDD Redding CA USA
HLN Helena MT USA
CPR Casper WY USA
FWA Fort Wayne IN USA
IMT Iron Mountain MI USA
DTW Detroit MI USA
BZN Bozeman MT USA
SBN South Bend IN USA
SPS Wichita Falls TX USA
BFL Bakersfield CA USA
HOB Hobbs NM USA
TVC Traverse City MI USA
CLE Cleveland OH USA
ABR Aberdeen SD USA
CHS Charleston SC USA
GUC Gunnison CO USA
IND Indianapolis IN USA
SDF Louisville KY USA
SAN San Diego CA USA
RSW Fort Myers FL USA
BOS Boston MA USA
TUL Tulsa OK USA
AGS Augusta GA USA
MOB Mobile AL USA
TUS Tucson AZ USA
KTN Ketchikan AK USA
BTR Baton Rouge LA USA
PNS Pensacola FL USA
ABQ Albuquerque NM USA
LGA New York NY USA
DAL Dallas TX USA
JNU Juneau AK USA
MAF Midland TX USA
RIC Richmond VA USA
FAR Fargo ND USA
MTJ Montrose CO USA
AMA Amarillo TX USA
ROC Rochester NY USA
SHV Shreveport LA USA
YAK Yakutat AK USA
CSG Columbus GA USA
ALO Waterloo IA USA
DRO Durango CO USA
CRP Corpus Christi TX USA
FNT Flint MI USA
GSO Greensboro NC USA
LWS Lewiston ID USA
TOL Toledo OH USA
GTF Great Falls MT USA
MKE Milwaukee WI USA
RKS Rock Springs WY USA
STL St. Louis MO USA
MHT Manchester NH USA
CRW Charleston WV USA
SLC Salt Lake City UT USA
ACV Eureka CA USA
DFW Dallas TX USA
OME Nome AK USA
ORF Norfolk VA USA
RDU Raleigh NC USA
SYR Syracuse NY USA
BQK Brunswick GA USA
ROA Roanoke VA USA
OKC Oklahoma City OK USA
EYW Key West FL USA
BOI Boise ID USA
ABY Albany GA USA
PIA Peoria IL USA
GRI Grand Island NE USA
PBI West Palm Beach FL USA
FSM Fort Smith AR USA
TYS Knoxville TN USA
DAB Daytona Beach FL USA
TTN Trenton NJ USA
MDT Harrisburg PA USA
AUS Austin TX USA
DCA Washington DC null USA
PIH Pocatello ID USA
GCC Gillette WY USA
BUR Burbank CA USA
GRK Killeen TX USA
LBB Lubbock TX USA
JAN Jackson MS USA
MSP Minneapolis MN USA
SAF Santa Fe NM USA
HPN White Plains NY USA
DHN Dothan AL USA
PSP Palm Springs CA USA
INL International Falls MN USA
CIC Chico CA USA
EGE Vail CO USA
CLD Carlsbad CA USA
RST Rochester MN USA
DEN Denver CO USA
EUG Eugene OR USA
LFT Lafayette LA USA
PVD Providence RI USA
DBQ Dubuque IA USA
SAV Savannah GA USA
SFO San Francisco CA USA
JAX Jacksonville FL USA
LIT Little Rock AR USA
IDA Idaho Falls ID USA
TYR Tyler TX USA
ANC Anchorage AK USA
HRL Harlingen TX USA
LMT Klamath Falls OR USA
PHF Newport News VA USA
HOU Houston TX USA
SPI Springfield IL USA
MOT Minot ND USA
BTM Butte MT USA
SMF Sacramento CA USA
HIB Hibbing MN USA
ROW Roswell NM USA
MBS Saginaw MI USA
ILM Wilmington NC USA
LGB Long Beach CA USA
IAD Washington DC null USA
ICT Wichita KS USA
BGR Bangor ME USA
ELP El Paso TX USA
SUX Sioux City IA USA
HSV Huntsville AL USA
SIT Sitka AK USA
CWA Wausau WI USA
LCH Lake Charles LA USA
CMI Champaign IL USA
ELM Elmira NY USA
CLL College Station TX USA
VPS Fort Walton Beach FL USA
MSN Madison WI USA
MHK Manhattan KS USA
OAJ Jacksonville NC USA
EKO Elko NV USA
FSD Sioux Falls SD USA
EWR Newark NJ USA
MEM Memphis TN USA
ADQ Kodiak AK USA
GGG Longview TX USA
BLI Bellingham WA USA
OMA Omaha NE USA
ATL Atlanta GA USA
SJC San Jose CA USA
SBA Santa Barbara CA USA
ONT Ontario CA USA
EAU Eau Claire WI USA
GPT Gulfport MS USA
SUN Sun Valley ID USA
CHO Charlottesville VA USA
MSO Missoula MT USA
CMX Hancock MI USA
ORD Chicago IL USA
EVV Evansville IN USA
MLU Monroe LA USA
LAW Lawton OK USA
BRW Barrow AK USA
SBP San Luis Obispo CA USA
LIH Lihue, Kauai HI USA
GJT Grand Junction CO USA
FAI Fairbanks AK USA
BIS Bismarck ND USA
SNA Orange County CA USA
LAR Laramie WY USA
JLN Joplin MO USA
LRD Laredo TX USA
LEX Lexington KY USA
SGU St. George UT USA
MCI Kansas City MO USA
AEX Alexandria LA USA
ISN Williston ND USA
TXK Texarkana AR USA
BIL Billings MT USA
CID Cedar Rapids IA USA
PDX Portland OR USA
ABE Allentown PA USA
DIK Dickinson ND USA
ART Watertown NY USA
GCK Garden City KS USA
BET Bethel AK USA
AVL Asheville NC USA
MCO Orlando FL USA
GSP Greenville SC USA
TWF Twin Falls ID USA
MKG Muskegon MI USA
FAY Fayetteville NC USA
SCE State College PA USA
EWN New Bern NC USA
XNA Fayetteville AR USA
MRY Monterey CA USA
MLB Melbourne FL USA
HNL Honolulu, Oahu HI USA
CVG Cincinnati OH USA
RAP Rapid City SD USA
AZO Kalamazoo MI USA
WRG Wrangell AK USA
ISP Islip NY USA
FLG Flagstaff AZ USA
BHM Birmingham AL USA
ALB Albany NY USA
SEA Seattle WA USA
GRR Grand Rapids MI USA
CHA Chattanooga TN USA
IAH Houston TX USA
SMX Santa Maria CA USA
MDW Chicago IL USA
MQT Marquette MI USA
LNK Lincoln NE USA
RDM Redmond OR USA
DLH Duluth MN USA
DSM Des Moines IA USA
OAK Oakland CA USA
PHL Philadelphia PA USA
FCA Kalispell MT USA
MFE McAllen TX USA
OGG Kahului, Maui HI USA
YUM Yuma AZ USA
BMI Bloomington IL USA
GEG Spokane WA USA
TLH Tallahassee FL USA
LSE La Crosse WI USA
MIA Miami FL USA
BRO Brownsville TX USA
JAC Jackson Hole WY USA
CDV Cordova AK USA
TRI Tri-City Airport TN USA
SWF Newburgh NY USA
MGM Montgomery AL USA
BWI Baltimore MD USA
SGF Springfield MO USA
GFK Grand Forks ND USA
GNV Gainesville FL USA
OTH North Bend OR USA
PIT Pittsburgh PA USA
BJI Bemidji MN USA
ASE Aspen CO USA
BUF Buffalo NY USA
COU Columbia MO USA
ABI Abilene TX USA
MLI Moline IL USA
// Edges
// The edges of our graph are the flights between airports
display(tripEdges)
tripid delay src dst city_dst state_dst
1011111.0 -5.0 MSP INL International Falls MN
1021111.0 7.0 MSP INL International Falls MN
1031111.0 0.0 MSP INL International Falls MN
1041925.0 0.0 MSP INL International Falls MN
1061115.0 33.0 MSP INL International Falls MN
1071115.0 23.0 MSP INL International Falls MN
1081115.0 -9.0 MSP INL International Falls MN
1091115.0 11.0 MSP INL International Falls MN
1101115.0 -3.0 MSP INL International Falls MN
1112015.0 -7.0 MSP INL International Falls MN
1121925.0 -5.0 MSP INL International Falls MN
1131115.0 -3.0 MSP INL International Falls MN
1141115.0 -6.0 MSP INL International Falls MN
1151115.0 -7.0 MSP INL International Falls MN
1161115.0 -3.0 MSP INL International Falls MN
1171115.0 4.0 MSP INL International Falls MN
1182015.0 -5.0 MSP INL International Falls MN
1191925.0 -7.0 MSP INL International Falls MN
1201115.0 -6.0 MSP INL International Falls MN
1211115.0 0.0 MSP INL International Falls MN
1221115.0 -4.0 MSP INL International Falls MN
1231115.0 -4.0 MSP INL International Falls MN
1241115.0 -3.0 MSP INL International Falls MN
1252015.0 -12.0 MSP INL International Falls MN
1261925.0 -5.0 MSP INL International Falls MN
1271115.0 0.0 MSP INL International Falls MN
1281115.0 -8.0 MSP INL International Falls MN
1291115.0 -2.0 MSP INL International Falls MN
1301115.0 0.0 MSP INL International Falls MN
1311115.0 -3.0 MSP INL International Falls MN
2012015.0 -4.0 MSP INL International Falls MN
2022015.0 0.0 MSP INL International Falls MN
2031115.0 -7.0 MSP INL International Falls MN
2041115.0 -6.0 MSP INL International Falls MN
2051115.0 -4.0 MSP INL International Falls MN
2061115.0 -2.0 MSP INL International Falls MN
2071115.0 -15.0 MSP INL International Falls MN
2082015.0 -4.0 MSP INL International Falls MN
2091925.0 1.0 MSP INL International Falls MN
2101115.0 -3.0 MSP INL International Falls MN
2111115.0 -7.0 MSP INL International Falls MN
2121115.0 -2.0 MSP INL International Falls MN
2131115.0 -3.0 MSP INL International Falls MN
2141115.0 -11.0 MSP INL International Falls MN
2152015.0 16.0 MSP INL International Falls MN
2161925.0 169.0 MSP INL International Falls MN
2171115.0 27.0 MSP INL International Falls MN
2181115.0 96.0 MSP INL International Falls MN
2191115.0 -9.0 MSP INL International Falls MN
2201115.0 -6.0 MSP INL International Falls MN
2211115.0 -4.0 MSP INL International Falls MN
2222015.0 -4.0 MSP INL International Falls MN
2231925.0 -3.0 MSP INL International Falls MN
2241115.0 -2.0 MSP INL International Falls MN
2251115.0 -6.0 MSP INL International Falls MN
2261115.0 -8.0 MSP INL International Falls MN
2271115.0 -8.0 MSP INL International Falls MN
2281115.0 5.0 MSP INL International Falls MN
3012015.0 -4.0 MSP INL International Falls MN
3022000.0 0.0 MSP INL International Falls MN
3031115.0 17.0 MSP INL International Falls MN
3041115.0 0.0 MSP INL International Falls MN
3051115.0 -7.0 MSP INL International Falls MN
3061115.0 -8.0 MSP INL International Falls MN
3071115.0 -10.0 MSP INL International Falls MN
3082000.0 -11.0 MSP INL International Falls MN
3092000.0 -9.0 MSP INL International Falls MN
3101115.0 -10.0 MSP INL International Falls MN
3111115.0 -8.0 MSP INL International Falls MN
3121115.0 -6.0 MSP INL International Falls MN
3131115.0 -8.0 MSP INL International Falls MN
3141115.0 -5.0 MSP INL International Falls MN
3152000.0 -11.0 MSP INL International Falls MN
3162000.0 -10.0 MSP INL International Falls MN
3171115.0 25.0 MSP INL International Falls MN
3181115.0 2.0 MSP INL International Falls MN
3191115.0 -5.0 MSP INL International Falls MN
3201115.0 -6.0 MSP INL International Falls MN
3211115.0 0.0 MSP INL International Falls MN
3222000.0 -10.0 MSP INL International Falls MN
3232000.0 -9.0 MSP INL International Falls MN
3241115.0 -9.0 MSP INL International Falls MN
3251115.0 -4.0 MSP INL International Falls MN
3261115.0 -5.0 MSP INL International Falls MN
3271115.0 9.0 MSP INL International Falls MN
3281115.0 -7.0 MSP INL International Falls MN
3292000.0 -19.0 MSP INL International Falls MN
3302000.0 -10.0 MSP INL International Falls MN
3311115.0 -8.0 MSP INL International Falls MN
2011230.0 -3.0 EWR MSY New Orleans LA
2010719.0 -2.0 EWR MSY New Orleans LA
2021230.0 -10.0 EWR MSY New Orleans LA
2020709.0 59.0 EWR MSY New Orleans LA
2021654.0 21.0 EWR MSY New Orleans LA
2030719.0 -6.0 EWR MSY New Orleans LA
2031659.0 0.0 EWR MSY New Orleans LA
2031230.0 0.0 EWR MSY New Orleans LA
2032043.0 0.0 EWR MSY New Orleans LA
2041230.0 24.0 EWR MSY New Orleans LA
2040719.0 168.0 EWR MSY New Orleans LA
2041730.0 88.0 EWR MSY New Orleans LA
2042043.0 106.0 EWR MSY New Orleans LA
2051659.0 0.0 EWR MSY New Orleans LA
2050719.0 0.0 EWR MSY New Orleans LA
2050929.0 0.0 EWR MSY New Orleans LA
2052043.0 46.0 EWR MSY New Orleans LA
2060719.0 -3.0 EWR MSY New Orleans LA
2061659.0 82.0 EWR MSY New Orleans LA
2061230.0 61.0 EWR MSY New Orleans LA
2062043.0 7.0 EWR MSY New Orleans LA
2070719.0 8.0 EWR MSY New Orleans LA
2071659.0 19.0 EWR MSY New Orleans LA
2071230.0 27.0 EWR MSY New Orleans LA
2072048.0 47.0 EWR MSY New Orleans LA
2081230.0 -10.0 EWR MSY New Orleans LA
2080719.0 -1.0 EWR MSY New Orleans LA
2091229.0 95.0 EWR MSY New Orleans LA
2091654.0 -5.0 EWR MSY New Orleans LA
2090709.0 -8.0 EWR MSY New Orleans LA
2092043.0 32.0 EWR MSY New Orleans LA
2100719.0 14.0 EWR MSY New Orleans LA
2101659.0 16.0 EWR MSY New Orleans LA
2101230.0 -4.0 EWR MSY New Orleans LA
2102043.0 -4.0 EWR MSY New Orleans LA
2111230.0 10.0 EWR MSY New Orleans LA
2110719.0 46.0 EWR MSY New Orleans LA
2111730.0 -9.0 EWR MSY New Orleans LA
2112043.0 -2.0 EWR MSY New Orleans LA
2120719.0 1.0 EWR MSY New Orleans LA
2121230.0 -4.0 EWR MSY New Orleans LA
2120929.0 89.0 EWR MSY New Orleans LA
2122043.0 36.0 EWR MSY New Orleans LA
2130738.0 0.0 EWR MSY New Orleans LA
2132041.0 0.0 EWR MSY New Orleans LA
2140729.0 0.0 EWR MSY New Orleans LA
2142041.0 0.0 EWR MSY New Orleans LA
2151206.0 0.0 EWR MSY New Orleans LA
2150659.0 0.0 EWR MSY New Orleans LA
2160705.0 -5.0 EWR MSY New Orleans LA
2170729.0 0.0 EWR MSY New Orleans LA
2172041.0 -7.0 EWR MSY New Orleans LA
2180738.0 0.0 EWR MSY New Orleans LA
2182041.0 36.0 EWR MSY New Orleans LA
2190727.0 15.0 EWR MSY New Orleans LA
2200738.0 -7.0 EWR MSY New Orleans LA
2202041.0 51.0 EWR MSY New Orleans LA
2210729.0 -2.0 EWR MSY New Orleans LA
2212041.0 0.0 EWR MSY New Orleans LA
2221206.0 -8.0 EWR MSY New Orleans LA
2220659.0 8.0 EWR MSY New Orleans LA
2232041.0 8.0 EWR MSY New Orleans LA
2230705.0 -10.0 EWR MSY New Orleans LA
2240729.0 6.0 EWR MSY New Orleans LA
2242041.0 -7.0 EWR MSY New Orleans LA
2250738.0 0.0 EWR MSY New Orleans LA
2260727.0 23.0 EWR MSY New Orleans LA
2262041.0 174.0 EWR MSY New Orleans LA
2270738.0 8.0 EWR MSY New Orleans LA
2272041.0 32.0 EWR MSY New Orleans LA
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1291025.0 1.0 LAS MSY New Orleans LA
1291750.0 -5.0 LAS MSY New Orleans LA
1301025.0 0.0 LAS MSY New Orleans LA
1301750.0 35.0 LAS MSY New Orleans LA
1311025.0 11.0 LAS MSY New Orleans LA
1311750.0 25.0 LAS MSY New Orleans LA
2011530.0 -3.0 MCI MSY New Orleans LA
2021105.0 -4.0 MCI MSY New Orleans LA
2031105.0 -1.0 MCI MSY New Orleans LA
2041105.0 1.0 MCI MSY New Orleans LA
2051105.0 6.0 MCI MSY New Orleans LA
2061105.0 40.0 MCI MSY New Orleans LA
2071105.0 7.0 MCI MSY New Orleans LA
2081530.0 2.0 MCI MSY New Orleans LA
2091105.0 -2.0 MCI MSY New Orleans LA
2101105.0 -2.0 MCI MSY New Orleans LA
2111105.0 -1.0 MCI MSY New Orleans LA
2121105.0 7.0 MCI MSY New Orleans LA
2130800.0 -5.0 MCI MSY New Orleans LA
2140830.0 3.0 MCI MSY New Orleans LA
2150750.0 7.0 MCI MSY New Orleans LA
2160930.0 -1.0 MCI MSY New Orleans LA
2170830.0 10.0 MCI MSY New Orleans LA
2180830.0 2.0 MCI MSY New Orleans LA
2190830.0 -4.0 MCI MSY New Orleans LA
2200830.0 9.0 MCI MSY New Orleans LA
2210830.0 -2.0 MCI MSY New Orleans LA
2220750.0 0.0 MCI MSY New Orleans LA
2230930.0 2.0 MCI MSY New Orleans LA
2240830.0 3.0 MCI MSY New Orleans LA
2250830.0 -5.0 MCI MSY New Orleans LA
2260830.0 251.0 MCI MSY New Orleans LA
2270830.0 -1.0 MCI MSY New Orleans LA
2280830.0 -2.0 MCI MSY New Orleans LA
3010750.0 0.0 MCI MSY New Orleans LA
3020930.0 35.0 MCI MSY New Orleans LA
3030830.0 1.0 MCI MSY New Orleans LA
3040830.0 11.0 MCI MSY New Orleans LA
3050830.0 2.0 MCI MSY New Orleans LA
3060830.0 -1.0 MCI MSY New Orleans LA
3070830.0 -2.0 MCI MSY New Orleans LA
3081610.0 93.0 MCI MSY New Orleans LA
3090950.0 -1.0 MCI MSY New Orleans LA
3100950.0 8.0 MCI MSY New Orleans LA
3110950.0 36.0 MCI MSY New Orleans LA
3120950.0 68.0 MCI MSY New Orleans LA
3130950.0 13.0 MCI MSY New Orleans LA
3140950.0 1.0 MCI MSY New Orleans LA
3151610.0 16.0 MCI MSY New Orleans LA
3160950.0 -5.0 MCI MSY New Orleans LA
3170950.0 -1.0 MCI MSY New Orleans LA
3180950.0 1.0 MCI MSY New Orleans LA
3190950.0 -1.0 MCI MSY New Orleans LA
3200950.0 3.0 MCI MSY New Orleans LA
3210950.0 7.0 MCI MSY New Orleans LA
3221610.0 38.0 MCI MSY New Orleans LA
3230950.0 -1.0 MCI MSY New Orleans LA
3240950.0 0.0 MCI MSY New Orleans LA
3250950.0 4.0 MCI MSY New Orleans LA
3260950.0 5.0 MCI MSY New Orleans LA
3270950.0 12.0 MCI MSY New Orleans LA
3280950.0 0.0 MCI MSY New Orleans LA
3291610.0 12.0 MCI MSY New Orleans LA
3300950.0 -2.0 MCI MSY New Orleans LA
3310950.0 3.0 MCI MSY New Orleans LA
1011635.0 -7.0 MCI MSY New Orleans LA
1021635.0 96.0 MCI MSY New Orleans LA
1031635.0 3.0 MCI MSY New Orleans LA
1041205.0 1.0 MCI MSY New Orleans LA
1051635.0 60.0 MCI MSY New Orleans LA
1061635.0 -7.0 MCI MSY New Orleans LA
1071105.0 14.0 MCI MSY New Orleans LA
1081105.0 4.0 MCI MSY New Orleans LA
1091105.0 11.0 MCI MSY New Orleans LA
1101105.0 -1.0 MCI MSY New Orleans LA
1111530.0 11.0 MCI MSY New Orleans LA
1121105.0 0.0 MCI MSY New Orleans LA
1131105.0 -5.0 MCI MSY New Orleans LA
1141105.0 1.0 MCI MSY New Orleans LA
1151105.0 9.0 MCI MSY New Orleans LA
1161105.0 1.0 MCI MSY New Orleans LA
1171105.0 -1.0 MCI MSY New Orleans LA
1181530.0 48.0 MCI MSY New Orleans LA
1191105.0 0.0 MCI MSY New Orleans LA
1201105.0 -4.0 MCI MSY New Orleans LA
1211105.0 2.0 MCI MSY New Orleans LA
1221105.0 19.0 MCI MSY New Orleans LA
1231105.0 -2.0 MCI MSY New Orleans LA
1241105.0 72.0 MCI MSY New Orleans LA
1251530.0 5.0 MCI MSY New Orleans LA
1261105.0 -5.0 MCI MSY New Orleans LA
1271105.0 -6.0 MCI MSY New Orleans LA
1281105.0 0.0 MCI MSY New Orleans LA
1291105.0 0.0 MCI MSY New Orleans LA
1301105.0 1.0 MCI MSY New Orleans LA
1311105.0 1.0 MCI MSY New Orleans LA
3011530.0 72.0 BNA MSY New Orleans LA
3010850.0 2.0 BNA MSY New Orleans LA
3011245.0 4.0 BNA MSY New Orleans LA
3021610.0 14.0 BNA MSY New Orleans LA
3021350.0 15.0 BNA MSY New Orleans LA
3021800.0 56.0 BNA MSY New Orleans LA
3031610.0 13.0 BNA MSY New Orleans LA
3030810.0 0.0 BNA MSY New Orleans LA
3031350.0 -1.0 BNA MSY New Orleans LA
3031800.0 -5.0 BNA MSY New Orleans LA
3041610.0 -3.0 BNA MSY New Orleans LA
3040810.0 -4.0 BNA MSY New Orleans LA
3041350.0 10.0 BNA MSY New Orleans LA
3041800.0 7.0 BNA MSY New Orleans LA
3051610.0 -1.0 BNA MSY New Orleans LA
3050810.0 11.0 BNA MSY New Orleans LA
3051350.0 48.0 BNA MSY New Orleans LA
3051800.0 21.0 BNA MSY New Orleans LA
3061610.0 26.0 BNA MSY New Orleans LA
3060810.0 -5.0 BNA MSY New Orleans LA
3061350.0 13.0 BNA MSY New Orleans LA
3061800.0 5.0 BNA MSY New Orleans LA
3071610.0 12.0 BNA MSY New Orleans LA
3070810.0 -3.0 BNA MSY New Orleans LA
3071350.0 10.0 BNA MSY New Orleans LA
3071800.0 7.0 BNA MSY New Orleans LA
3081540.0 27.0 BNA MSY New Orleans LA
3081335.0 -4.0 BNA MSY New Orleans LA
3080945.0 11.0 BNA MSY New Orleans LA
3091620.0 0.0 BNA MSY New Orleans LA
3091820.0 25.0 BNA MSY New Orleans LA
3091420.0 12.0 BNA MSY New Orleans LA
3100820.0 -1.0 BNA MSY New Orleans LA
3101420.0 41.0 BNA MSY New Orleans LA
3101820.0 11.0 BNA MSY New Orleans LA
3101620.0 7.0 BNA MSY New Orleans LA
3110820.0 3.0 BNA MSY New Orleans LA
3111420.0 15.0 BNA MSY New Orleans LA
3111820.0 29.0 BNA MSY New Orleans LA
3111620.0 5.0 BNA MSY New Orleans LA
3120820.0 12.0 BNA MSY New Orleans LA
3121420.0 40.0 BNA MSY New Orleans LA
3121820.0 15.0 BNA MSY New Orleans LA
3121620.0 24.0 BNA MSY New Orleans LA
3130820.0 126.0 BNA MSY New Orleans LA
3131420.0 13.0 BNA MSY New Orleans LA
3131820.0 55.0 BNA MSY New Orleans LA
3131620.0 40.0 BNA MSY New Orleans LA
3140820.0 -2.0 BNA MSY New Orleans LA
3141420.0 35.0 BNA MSY New Orleans LA
3141820.0 21.0 BNA MSY New Orleans LA
3141620.0 36.0 BNA MSY New Orleans LA
3151335.0 -3.0 BNA MSY New Orleans LA
3150945.0 3.0 BNA MSY New Orleans LA
3151540.0 -3.0 BNA MSY New Orleans LA
3161620.0 22.0 BNA MSY New Orleans LA
3161820.0 39.0 BNA MSY New Orleans LA
3161420.0 0.0 BNA MSY New Orleans LA
3170820.0 1.0 BNA MSY New Orleans LA
3171420.0 112.0 BNA MSY New Orleans LA
3171820.0 12.0 BNA MSY New Orleans LA
3171620.0 56.0 BNA MSY New Orleans LA
3180820.0 0.0 BNA MSY New Orleans LA
3181420.0 25.0 BNA MSY New Orleans LA
3181820.0 36.0 BNA MSY New Orleans LA
3181620.0 1.0 BNA MSY New Orleans LA
3190820.0 -2.0 BNA MSY New Orleans LA
3191420.0 54.0 BNA MSY New Orleans LA
3191820.0 7.0 BNA MSY New Orleans LA
3191620.0 29.0 BNA MSY New Orleans LA
3200820.0 0.0 BNA MSY New Orleans LA
3201420.0 18.0 BNA MSY New Orleans LA
3201820.0 9.0 BNA MSY New Orleans LA
3201620.0 79.0 BNA MSY New Orleans LA
3210820.0 3.0 BNA MSY New Orleans LA
3211420.0 22.0 BNA MSY New Orleans LA
3211820.0 30.0 BNA MSY New Orleans LA
3211620.0 22.0 BNA MSY New Orleans LA
3221335.0 -2.0 BNA MSY New Orleans LA
3220945.0 0.0 BNA MSY New Orleans LA
3221540.0 -1.0 BNA MSY New Orleans LA
3231620.0 -2.0 BNA MSY New Orleans LA
3231820.0 6.0 BNA MSY New Orleans LA
3231420.0 -3.0 BNA MSY New Orleans LA
3240820.0 0.0 BNA MSY New Orleans LA
3241420.0 27.0 BNA MSY New Orleans LA
3241820.0 44.0 BNA MSY New Orleans LA
3241620.0 41.0 BNA MSY New Orleans LA
3250820.0 0.0 BNA MSY New Orleans LA
3251420.0 70.0 BNA MSY New Orleans LA
3251820.0 30.0 BNA MSY New Orleans LA
3251620.0 30.0 BNA MSY New Orleans LA
3260820.0 -1.0 BNA MSY New Orleans LA
3261420.0 8.0 BNA MSY New Orleans LA
3261820.0 1.0 BNA MSY New Orleans LA
3261620.0 -4.0 BNA MSY New Orleans LA
3270820.0 0.0 BNA MSY New Orleans LA
3271420.0 25.0 BNA MSY New Orleans LA
3271820.0 41.0 BNA MSY New Orleans LA
3271620.0 23.0 BNA MSY New Orleans LA
3280820.0 -5.0 BNA MSY New Orleans LA
3281420.0 52.0 BNA MSY New Orleans LA
3281820.0 17.0 BNA MSY New Orleans LA
3281620.0 15.0 BNA MSY New Orleans LA
3291335.0 1.0 BNA MSY New Orleans LA
3290945.0 20.0 BNA MSY New Orleans LA
3291540.0 35.0 BNA MSY New Orleans LA
3301620.0 0.0 BNA MSY New Orleans LA
3301820.0 22.0 BNA MSY New Orleans LA
3301420.0 10.0 BNA MSY New Orleans LA
3310820.0 -1.0 BNA MSY New Orleans LA
3311420.0 19.0 BNA MSY New Orleans LA
3311820.0 25.0 BNA MSY New Orleans LA
3311620.0 30.0 BNA MSY New Orleans LA
1010800.0 -3.0 BNA MSY New Orleans LA
1011210.0 7.0 BNA MSY New Orleans LA
1011835.0 53.0 BNA MSY New Orleans LA
1021215.0 43.0 BNA MSY New Orleans LA
1021835.0 200.0 BNA MSY New Orleans LA
1020800.0 29.0 BNA MSY New Orleans LA
1031215.0 185.0 BNA MSY New Orleans LA
1031835.0 226.0 BNA MSY New Orleans LA
1030800.0 -1.0 BNA MSY New Orleans LA
1041420.0 174.0 BNA MSY New Orleans LA
1040835.0 18.0 BNA MSY New Orleans LA
1051215.0 85.0 BNA MSY New Orleans LA
1051835.0 283.0 BNA MSY New Orleans LA
1050800.0 3.0 BNA MSY New Orleans LA
1061215.0 150.0 BNA MSY New Orleans LA
1061835.0 133.0 BNA MSY New Orleans LA
1060800.0 102.0 BNA MSY New Orleans LA
1071240.0 57.0 BNA MSY New Orleans LA
1071455.0 12.0 BNA MSY New Orleans LA
1070905.0 5.0 BNA MSY New Orleans LA
1071735.0 131.0 BNA MSY New Orleans LA
1081240.0 19.0 BNA MSY New Orleans LA
1081455.0 2.0 BNA MSY New Orleans LA
1080905.0 -2.0 BNA MSY New Orleans LA
1081735.0 34.0 BNA MSY New Orleans LA
1091240.0 14.0 BNA MSY New Orleans LA
1091455.0 24.0 BNA MSY New Orleans LA
1090905.0 -1.0 BNA MSY New Orleans LA
1091735.0 28.0 BNA MSY New Orleans LA
1101240.0 50.0 BNA MSY New Orleans LA
1101455.0 11.0 BNA MSY New Orleans LA
1100905.0 4.0 BNA MSY New Orleans LA
1101735.0 33.0 BNA MSY New Orleans LA
1111305.0 0.0 BNA MSY New Orleans LA
1111805.0 2.0 BNA MSY New Orleans LA
1110950.0 0.0 BNA MSY New Orleans LA
1121235.0 8.0 BNA MSY New Orleans LA
1121455.0 4.0 BNA MSY New Orleans LA
1121735.0 4.0 BNA MSY New Orleans LA
1131240.0 9.0 BNA MSY New Orleans LA
1131455.0 2.0 BNA MSY New Orleans LA
1130850.0 -1.0 BNA MSY New Orleans LA
1131735.0 15.0 BNA MSY New Orleans LA
1141240.0 17.0 BNA MSY New Orleans LA
1141455.0 -1.0 BNA MSY New Orleans LA
1140850.0 -4.0 BNA MSY New Orleans LA
1141735.0 7.0 BNA MSY New Orleans LA
1151240.0 -2.0 BNA MSY New Orleans LA
1151455.0 1.0 BNA MSY New Orleans LA
1150850.0 -2.0 BNA MSY New Orleans LA
1151735.0 9.0 BNA MSY New Orleans LA
1161240.0 17.0 BNA MSY New Orleans LA
1161455.0 17.0 BNA MSY New Orleans LA
1160850.0 -2.0 BNA MSY New Orleans LA
1161735.0 52.0 BNA MSY New Orleans LA
1171240.0 21.0 BNA MSY New Orleans LA
1171455.0 13.0 BNA MSY New Orleans LA
1170850.0 10.0 BNA MSY New Orleans LA
1171735.0 40.0 BNA MSY New Orleans LA
1181305.0 2.0 BNA MSY New Orleans LA
1181805.0 42.0 BNA MSY New Orleans LA
1180950.0 4.0 BNA MSY New Orleans LA
1191235.0 23.0 BNA MSY New Orleans LA
1191455.0 4.0 BNA MSY New Orleans LA
1191735.0 64.0 BNA MSY New Orleans LA
1201240.0 8.0 BNA MSY New Orleans LA
1201455.0 5.0 BNA MSY New Orleans LA
1200850.0 7.0 BNA MSY New Orleans LA
1201735.0 -3.0 BNA MSY New Orleans LA
1211240.0 41.0 BNA MSY New Orleans LA
1211455.0 -1.0 BNA MSY New Orleans LA
1210850.0 18.0 BNA MSY New Orleans LA
1211735.0 17.0 BNA MSY New Orleans LA
1221240.0 19.0 BNA MSY New Orleans LA
1221455.0 -1.0 BNA MSY New Orleans LA
1220850.0 -4.0 BNA MSY New Orleans LA
1221735.0 118.0 BNA MSY New Orleans LA
1231240.0 20.0 BNA MSY New Orleans LA
1231455.0 4.0 BNA MSY New Orleans LA
1230850.0 18.0 BNA MSY New Orleans LA
1231735.0 33.0 BNA MSY New Orleans LA
1241240.0 20.0 BNA MSY New Orleans LA
1241455.0 4.0 BNA MSY New Orleans LA
1240850.0 12.0 BNA MSY New Orleans LA
1241735.0 0.0 BNA MSY New Orleans LA
1251305.0 27.0 BNA MSY New Orleans LA
1251805.0 19.0 BNA MSY New Orleans LA
1250950.0 -2.0 BNA MSY New Orleans LA
1261235.0 0.0 BNA MSY New Orleans LA
1261455.0 5.0 BNA MSY New Orleans LA
1261735.0 3.0 BNA MSY New Orleans LA
1271240.0 17.0 BNA MSY New Orleans LA
1271455.0 -3.0 BNA MSY New Orleans LA
1270850.0 -2.0 BNA MSY New Orleans LA
1271735.0 10.0 BNA MSY New Orleans LA
1281240.0 0.0 BNA MSY New Orleans LA
1281455.0 0.0 BNA MSY New Orleans LA
1280850.0 0.0 BNA MSY New Orleans LA
1281735.0 0.0 BNA MSY New Orleans LA
1291240.0 13.0 BNA MSY New Orleans LA
1291455.0 -2.0 BNA MSY New Orleans LA
1290850.0 0.0 BNA MSY New Orleans LA
1291735.0 9.0 BNA MSY New Orleans LA
1301240.0 38.0 BNA MSY New Orleans LA
1301455.0 6.0 BNA MSY New Orleans LA
1300850.0 -1.0 BNA MSY New Orleans LA
1301735.0 57.0 BNA MSY New Orleans LA
1311240.0 31.0 BNA MSY New Orleans LA
1311455.0 22.0 BNA MSY New Orleans LA
1310850.0 -2.0 BNA MSY New Orleans LA
1311735.0 6.0 BNA MSY New Orleans LA
2011305.0 -1.0 BNA MSY New Orleans LA
2011805.0 -6.0 BNA MSY New Orleans LA
2010950.0 4.0 BNA MSY New Orleans LA
2021455.0 11.0 BNA MSY New Orleans LA
2021235.0 26.0 BNA MSY New Orleans LA
2021650.0 77.0 BNA MSY New Orleans LA
2031240.0 30.0 BNA MSY New Orleans LA
2031455.0 10.0 BNA MSY New Orleans LA
2030850.0 -1.0 BNA MSY New Orleans LA
2031735.0 -3.0 BNA MSY New Orleans LA
2041240.0 56.0 BNA MSY New Orleans LA
2041455.0 23.0 BNA MSY New Orleans LA
2040850.0 -1.0 BNA MSY New Orleans LA
2041735.0 3.0 BNA MSY New Orleans LA
2051240.0 33.0 BNA MSY New Orleans LA
2051455.0 14.0 BNA MSY New Orleans LA
2050850.0 19.0 BNA MSY New Orleans LA
2051735.0 26.0 BNA MSY New Orleans LA
2061240.0 43.0 BNA MSY New Orleans LA
2061455.0 -2.0 BNA MSY New Orleans LA
2060850.0 10.0 BNA MSY New Orleans LA
2061735.0 34.0 BNA MSY New Orleans LA
2071240.0 88.0 BNA MSY New Orleans LA
2071455.0 5.0 BNA MSY New Orleans LA
2070850.0 1.0 BNA MSY New Orleans LA
2071735.0 20.0 BNA MSY New Orleans LA
2081305.0 -6.0 BNA MSY New Orleans LA
2081805.0 0.0 BNA MSY New Orleans LA
2080950.0 -3.0 BNA MSY New Orleans LA
2091235.0 5.0 BNA MSY New Orleans LA
2091455.0 2.0 BNA MSY New Orleans LA
2091735.0 8.0 BNA MSY New Orleans LA
2101240.0 25.0 BNA MSY New Orleans LA
2101455.0 14.0 BNA MSY New Orleans LA
2100850.0 9.0 BNA MSY New Orleans LA
2101735.0 -2.0 BNA MSY New Orleans LA
2111240.0 145.0 BNA MSY New Orleans LA
2111455.0 -2.0 BNA MSY New Orleans LA
2110850.0 96.0 BNA MSY New Orleans LA
2111735.0 25.0 BNA MSY New Orleans LA
2121240.0 8.0 BNA MSY New Orleans LA
2121455.0 29.0 BNA MSY New Orleans LA
2120850.0 3.0 BNA MSY New Orleans LA
2121735.0 39.0 BNA MSY New Orleans LA
2131350.0 5.0 BNA MSY New Orleans LA
2131610.0 11.0 BNA MSY New Orleans LA
2130810.0 -4.0 BNA MSY New Orleans LA
2131800.0 9.0 BNA MSY New Orleans LA
2141610.0 37.0 BNA MSY New Orleans LA
2140810.0 13.0 BNA MSY New Orleans LA
2141350.0 46.0 BNA MSY New Orleans LA
2141800.0 21.0 BNA MSY New Orleans LA
// Build `tripGraph` GraphFrame
// This GraphFrame builds up on the vertices and edges based on our trips (flights)
val tripGraph = GraphFrame(tripVertices, tripEdges)
println(tripGraph)

// Build `tripGraphPrime` GraphFrame
// This graphframe contains a smaller subset of data to make it easier to display motifs and subgraphs (below)
val tripEdgesPrime = departureDelays_geo.select("tripid", "delay", "src", "dst")
val tripGraphPrime = GraphFrame(tripVertices, tripEdgesPrime)
GraphFrame(v:[id: string, City: string ... 2 more fields], e:[src: string, dst: string ... 4 more fields])
tripGraph: org.graphframes.GraphFrame = GraphFrame(v:[id: string, City: string ... 2 more fields], e:[src: string, dst: string ... 4 more fields])
tripEdgesPrime: org.apache.spark.sql.DataFrame = [tripid: int, delay: int ... 2 more fields]
tripGraphPrime: org.graphframes.GraphFrame = GraphFrame(v:[id: string, City: string ... 2 more fields], e:[src: string, dst: string ... 2 more fields])

Simple Queries

Let's start with a set of simple graph queries to understand flight performance and departure delays

println(s"Airports: ${tripGraph.vertices.count()}")
println(s"Trips: ${tripGraph.edges.count()}")
Airports: 279
Trips: 1361141
// Finding the longest Delay
val longestDelay = tripGraph.edges.groupBy().max("delay")
display(longestDelay)
max(delay)
1642.0
1642.0/60.0
res13: Double = 27.366666666666667
// Determining number of on-time / early flights vs. delayed flights
println(s"On-time / Early Flights: ${tripGraph.edges.filter("delay <= 0").count()}")
println(s"Delayed Flights: ${tripGraph.edges.filter("delay > 0").count()}")
On-time / Early Flights: 780469
Delayed Flights: 580672

What flights departing SFO are most likely to have significant delays

Note, delay can be <= 0 meaning the flight left on time or early

//tripGraph.createOrReplaceTempView("tripgraph")
val sfoDelayedTrips = tripGraph.edges.
  filter("src = 'SFO' and delay > 0").
  groupBy("src", "dst").
  avg("delay").
  sort(desc("avg(delay)"))
sfoDelayedTrips: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [src: string, dst: string ... 1 more field]
display(sfoDelayedTrips)
src dst avg(delay)
SFO OKC 59.073170731707314
SFO JAC 57.13333333333333
SFO COS 53.976190476190474
SFO OTH 48.09090909090909
SFO SAT 47.625
SFO MOD 46.80952380952381
SFO SUN 46.723404255319146
SFO CIC 46.72164948453608
SFO ABQ 44.8125
SFO ASE 44.285714285714285
SFO PIT 43.875
SFO MIA 43.81730769230769
SFO FAT 43.23972602739726
SFO MFR 43.11848341232228
SFO SBP 43.09770114942529
SFO MSP 42.766917293233085
SFO BOI 42.65482233502538
SFO RDM 41.98823529411764
SFO AUS 41.690677966101696
SFO SLC 41.407272727272726
SFO JFK 41.01379310344828
SFO PSP 40.909909909909906
SFO PHX 40.67272727272727
SFO MRY 40.61764705882353
SFO ACV 40.3728813559322
SFO LAS 40.107602339181284
SFO TUS 39.853658536585364
SFO SAN 38.97361809045226
SFO SBA 38.758620689655174
SFO BFL 38.51136363636363
SFO RDU 38.170731707317074
SFO STL 38.13513513513514
SFO IND 38.114285714285714
SFO EUG 37.573913043478264
SFO RNO 36.81372549019608
SFO BUR 36.75675675675676
SFO LGB 36.752941176470586
SFO HNL 36.25367647058823
SFO LAX 36.165543071161046
SFO RDD 36.11009174311926
SFO MSY 35.421052631578945
SFO SMF 34.936
SFO MDW 34.824742268041234
SFO FLL 34.76842105263158
SFO SEA 34.68854961832061
SFO MCI 34.68571428571428
SFO DFW 34.36642599277978
SFO OGG 34.171875
SFO PDX 34.14430894308943
SFO ORD 33.991130820399114
SFO LIH 32.93023255813954
SFO DEN 32.861491628614914
SFO PSC 32.604651162790695
SFO PHL 32.440677966101696
SFO BWI 31.70212765957447
SFO ONT 31.49079754601227
SFO SNA 31.18426103646833
SFO MCO 31.03488372093023
SFO MKE 31.03448275862069
SFO CLE 30.979591836734695
SFO EWR 30.354285714285716
SFO BOS 29.623471882640587
SFO LMT 29.233333333333334
SFO DTW 28.34722222222222
SFO IAH 28.322105263157894
SFO CVG 27.03125
SFO ATL 26.84860557768924
SFO IAD 26.125964010282775
SFO ANC 25.5
SFO BZN 23.964285714285715
SFO CLT 22.636363636363637
SFO DCA 21.896103896103895
// After displaying tripDelays, use Plot Options to set `state_dst` as a Key.
val tripDelays = tripGraph.edges.filter($"delay" > 0)
display(tripDelays)
tripid delay src dst city_dst state_dst
1021111.0 7.0 MSP INL International Falls MN
1061115.0 33.0 MSP INL International Falls MN
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1171115.0 4.0 MSP INL International Falls MN
2091925.0 1.0 MSP INL International Falls MN
2152015.0 16.0 MSP INL International Falls MN
2161925.0 169.0 MSP INL International Falls MN
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2181115.0 96.0 MSP INL International Falls MN
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3171115.0 25.0 MSP INL International Falls MN
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2020709.0 59.0 EWR MSY New Orleans LA
2021654.0 21.0 EWR MSY New Orleans LA
2041230.0 24.0 EWR MSY New Orleans LA
2040719.0 168.0 EWR MSY New Orleans LA
2041730.0 88.0 EWR MSY New Orleans LA
2042043.0 106.0 EWR MSY New Orleans LA
2052043.0 46.0 EWR MSY New Orleans LA
2061659.0 82.0 EWR MSY New Orleans LA
2061230.0 61.0 EWR MSY New Orleans LA
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2072048.0 47.0 EWR MSY New Orleans LA
2091229.0 95.0 EWR MSY New Orleans LA
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2120929.0 89.0 EWR MSY New Orleans LA
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2202041.0 51.0 EWR MSY New Orleans LA
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2262041.0 174.0 EWR MSY New Orleans LA
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2272041.0 32.0 EWR MSY New Orleans LA
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2282041.0 49.0 EWR MSY New Orleans LA
2281000.0 2.0 EWR MSY New Orleans LA
2051230.0 216.0 EWR MSY New Orleans LA
2131536.0 273.0 EWR MSY New Orleans LA
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2151902.0 31.0 EWR MSY New Orleans LA
2151536.0 66.0 EWR MSY New Orleans LA
2161536.0 7.0 EWR MSY New Orleans LA
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2181536.0 26.0 EWR MSY New Orleans LA
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2221536.0 65.0 EWR MSY New Orleans LA
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2191635.0 21.0 EWR MSY New Orleans LA
2211635.0 292.0 EWR MSY New Orleans LA
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3032041.0 113.0 EWR MSY New Orleans LA
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3061252.0 67.0 EWR MSY New Orleans LA
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3112059.0 181.0 EWR MSY New Orleans LA
3122059.0 22.0 EWR MSY New Orleans LA
3121252.0 161.0 EWR MSY New Orleans LA
3140705.0 66.0 EWR MSY New Orleans LA
3141252.0 39.0 EWR MSY New Orleans LA
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3151250.0 34.0 EWR MSY New Orleans LA
3171252.0 22.0 EWR MSY New Orleans LA
3172059.0 132.0 EWR MSY New Orleans LA
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3192059.0 16.0 EWR MSY New Orleans LA
3202059.0 77.0 EWR MSY New Orleans LA
3211252.0 9.0 EWR MSY New Orleans LA
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3252059.0 121.0 EWR MSY New Orleans LA
3262059.0 49.0 EWR MSY New Orleans LA
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3301255.0 64.0 EWR MSY New Orleans LA
3302059.0 166.0 EWR MSY New Orleans LA
3311252.0 12.0 EWR MSY New Orleans LA
3312059.0 7.0 EWR MSY New Orleans LA
3011902.0 64.0 EWR MSY New Orleans LA
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3260659.0 63.0 EWR MSY New Orleans LA
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3091825.0 45.0 EWR MSY New Orleans LA
3101825.0 10.0 EWR MSY New Orleans LA
3111825.0 5.0 EWR MSY New Orleans LA
3131825.0 123.0 EWR MSY New Orleans LA
3141825.0 6.0 EWR MSY New Orleans LA
3161825.0 24.0 EWR MSY New Orleans LA
3171825.0 6.0 EWR MSY New Orleans LA
3191825.0 223.0 EWR MSY New Orleans LA
3201825.0 178.0 EWR MSY New Orleans LA
3251825.0 222.0 EWR MSY New Orleans LA
3261825.0 51.0 EWR MSY New Orleans LA
3281825.0 26.0 EWR MSY New Orleans LA
3301825.0 139.0 EWR MSY New Orleans LA
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1071730.0 161.0 EWR MSY New Orleans LA
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1101659.0 244.0 EWR MSY New Orleans LA
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1211230.0 102.0 EWR MSY New Orleans LA
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1231659.0 94.0 EWR MSY New Orleans LA
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1241659.0 84.0 EWR MSY New Orleans LA
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1261654.0 113.0 EWR MSY New Orleans LA
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1011815.0 125.0 EWR MSY New Orleans LA
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1051815.0 172.0 EWR MSY New Orleans LA
1061815.0 151.0 EWR MSY New Orleans LA
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1081815.0 14.0 EWR MSY New Orleans LA
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1161815.0 8.0 EWR MSY New Orleans LA
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1191815.0 5.0 EWR MSY New Orleans LA
1201815.0 5.0 EWR MSY New Orleans LA
1221815.0 3.0 EWR MSY New Orleans LA
1241815.0 84.0 EWR MSY New Orleans LA
2021025.0 3.0 LAS MSY New Orleans LA
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2051750.0 29.0 LAS MSY New Orleans LA
2061025.0 1.0 LAS MSY New Orleans LA
2061750.0 48.0 LAS MSY New Orleans LA
2071750.0 20.0 LAS MSY New Orleans LA
2081055.0 2.0 LAS MSY New Orleans LA
2091750.0 33.0 LAS MSY New Orleans LA
2111025.0 15.0 LAS MSY New Orleans LA
2121750.0 158.0 LAS MSY New Orleans LA
2131855.0 11.0 LAS MSY New Orleans LA
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2141855.0 22.0 LAS MSY New Orleans LA
2141215.0 18.0 LAS MSY New Orleans LA
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2161855.0 58.0 LAS MSY New Orleans LA
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2181215.0 58.0 LAS MSY New Orleans LA
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2221635.0 133.0 LAS MSY New Orleans LA
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2241215.0 16.0 LAS MSY New Orleans LA
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2271215.0 32.0 LAS MSY New Orleans LA
2281855.0 61.0 LAS MSY New Orleans LA
2281215.0 94.0 LAS MSY New Orleans LA
3010935.0 10.0 LAS MSY New Orleans LA
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3051215.0 27.0 LAS MSY New Orleans LA
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3071855.0 36.0 LAS MSY New Orleans LA
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3101905.0 49.0 LAS MSY New Orleans LA
3111905.0 9.0 LAS MSY New Orleans LA
3110840.0 84.0 LAS MSY New Orleans LA
3121905.0 26.0 LAS MSY New Orleans LA
3131905.0 37.0 LAS MSY New Orleans LA
3130840.0 1.0 LAS MSY New Orleans LA
3141905.0 14.0 LAS MSY New Orleans LA
3150830.0 16.0 LAS MSY New Orleans LA
3151940.0 95.0 LAS MSY New Orleans LA
3171905.0 13.0 LAS MSY New Orleans LA
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3181905.0 52.0 LAS MSY New Orleans LA
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3201905.0 36.0 LAS MSY New Orleans LA
3200840.0 68.0 LAS MSY New Orleans LA
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3230840.0 16.0 LAS MSY New Orleans LA
3241905.0 9.0 LAS MSY New Orleans LA
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3251905.0 10.0 LAS MSY New Orleans LA
3261905.0 14.0 LAS MSY New Orleans LA
3260840.0 3.0 LAS MSY New Orleans LA
3271905.0 13.0 LAS MSY New Orleans LA
3280840.0 33.0 LAS MSY New Orleans LA
3291940.0 231.0 LAS MSY New Orleans LA
3301905.0 7.0 LAS MSY New Orleans LA
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1011755.0 160.0 LAS MSY New Orleans LA
1021805.0 138.0 LAS MSY New Orleans LA
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1031805.0 154.0 LAS MSY New Orleans LA
1030905.0 179.0 LAS MSY New Orleans LA
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1051805.0 53.0 LAS MSY New Orleans LA
1061755.0 61.0 LAS MSY New Orleans LA
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1071025.0 1.0 LAS MSY New Orleans LA
1071750.0 302.0 LAS MSY New Orleans LA
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1081750.0 52.0 LAS MSY New Orleans LA
1091750.0 8.0 LAS MSY New Orleans LA
1101750.0 92.0 LAS MSY New Orleans LA
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1141750.0 127.0 LAS MSY New Orleans LA
1151025.0 1.0 LAS MSY New Orleans LA
1171025.0 12.0 LAS MSY New Orleans LA
1191025.0 3.0 LAS MSY New Orleans LA
1201750.0 6.0 LAS MSY New Orleans LA
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1231750.0 30.0 LAS MSY New Orleans LA
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1261750.0 27.0 LAS MSY New Orleans LA
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1301750.0 35.0 LAS MSY New Orleans LA
1311025.0 11.0 LAS MSY New Orleans LA
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2041105.0 1.0 MCI MSY New Orleans LA
2051105.0 6.0 MCI MSY New Orleans LA
2061105.0 40.0 MCI MSY New Orleans LA
2071105.0 7.0 MCI MSY New Orleans LA
2081530.0 2.0 MCI MSY New Orleans LA
2121105.0 7.0 MCI MSY New Orleans LA
2140830.0 3.0 MCI MSY New Orleans LA
2150750.0 7.0 MCI MSY New Orleans LA
2170830.0 10.0 MCI MSY New Orleans LA
2180830.0 2.0 MCI MSY New Orleans LA
2200830.0 9.0 MCI MSY New Orleans LA
2230930.0 2.0 MCI MSY New Orleans LA
2240830.0 3.0 MCI MSY New Orleans LA
2260830.0 251.0 MCI MSY New Orleans LA
3020930.0 35.0 MCI MSY New Orleans LA
3030830.0 1.0 MCI MSY New Orleans LA
3040830.0 11.0 MCI MSY New Orleans LA
3050830.0 2.0 MCI MSY New Orleans LA
3081610.0 93.0 MCI MSY New Orleans LA
3100950.0 8.0 MCI MSY New Orleans LA
3110950.0 36.0 MCI MSY New Orleans LA
3120950.0 68.0 MCI MSY New Orleans LA
3130950.0 13.0 MCI MSY New Orleans LA
3140950.0 1.0 MCI MSY New Orleans LA
3151610.0 16.0 MCI MSY New Orleans LA
3180950.0 1.0 MCI MSY New Orleans LA
3200950.0 3.0 MCI MSY New Orleans LA
3210950.0 7.0 MCI MSY New Orleans LA
3221610.0 38.0 MCI MSY New Orleans LA
3250950.0 4.0 MCI MSY New Orleans LA
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3270950.0 12.0 MCI MSY New Orleans LA
3291610.0 12.0 MCI MSY New Orleans LA
3310950.0 3.0 MCI MSY New Orleans LA
1021635.0 96.0 MCI MSY New Orleans LA
1031635.0 3.0 MCI MSY New Orleans LA
1041205.0 1.0 MCI MSY New Orleans LA
1051635.0 60.0 MCI MSY New Orleans LA
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1241105.0 72.0 MCI MSY New Orleans LA
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1301105.0 1.0 MCI MSY New Orleans LA
1311105.0 1.0 MCI MSY New Orleans LA
3011530.0 72.0 BNA MSY New Orleans LA
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3050810.0 11.0 BNA MSY New Orleans LA
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3111420.0 15.0 BNA MSY New Orleans LA
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3121620.0 24.0 BNA MSY New Orleans LA
3130820.0 126.0 BNA MSY New Orleans LA
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3141420.0 35.0 BNA MSY New Orleans LA
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3141620.0 36.0 BNA MSY New Orleans LA
3150945.0 3.0 BNA MSY New Orleans LA
3161620.0 22.0 BNA MSY New Orleans LA
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3171420.0 112.0 BNA MSY New Orleans LA
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3171620.0 56.0 BNA MSY New Orleans LA
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3201620.0 79.0 BNA MSY New Orleans LA
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3251420.0 70.0 BNA MSY New Orleans LA
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1021835.0 200.0 BNA MSY New Orleans LA
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1051835.0 283.0 BNA MSY New Orleans LA
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1131535.0 3.0 DAL MSY New Orleans LA
1130630.0 2.0 DAL MSY New Orleans LA
1130925.0 9.0 DAL MSY New Orleans LA
1131025.0 18.0 DAL MSY New Orleans LA
1142015.0 10.0 DAL MSY New Orleans LA
1140630.0 5.0 DAL MSY New Orleans LA
1140925.0 12.0 DAL MSY New Orleans LA
1141025.0 16.0 DAL MSY New Orleans LA
1141230.0 3.0 DAL MSY New Orleans LA
1141635.0 5.0 DAL MSY New Orleans LA
1151930.0 1.0 DAL MSY New Orleans LA
1150925.0 8.0 DAL MSY New Orleans LA
1151025.0 19.0 DAL MSY New Orleans LA
1162015.0 6.0 DAL MSY New Orleans LA
1161535.0 26.0 DAL MSY New Orleans LA
1161930.0 5.0 DAL MSY New Orleans LA
1160925.0 10.0 DAL MSY New Orleans LA
1161025.0 23.0 DAL MSY New Orleans LA
1161230.0 4.0 DAL MSY New Orleans LA
1161635.0 28.0 DAL MSY New Orleans LA
1172015.0 17.0 DAL MSY New Orleans LA
1171535.0 2.0 DAL MSY New Orleans LA
1171025.0 3.0 DAL MSY New Orleans LA
1171230.0 17.0 DAL MSY New Orleans LA
1171635.0 30.0 DAL MSY New Orleans LA
1180645.0 19.0 DAL MSY New Orleans LA
1181450.0 3.0 DAL MSY New Orleans LA
1181625.0 7.0 DAL MSY New Orleans LA
1191535.0 23.0 DAL MSY New Orleans LA
1191620.0 4.0 DAL MSY New Orleans LA
1191930.0 219.0 DAL MSY New Orleans LA
1190925.0 5.0 DAL MSY New Orleans LA
1200925.0 12.0 DAL MSY New Orleans LA
1201025.0 33.0 DAL MSY New Orleans LA
1201230.0 1.0 DAL MSY New Orleans LA
1201635.0 6.0 DAL MSY New Orleans LA
1211535.0 95.0 DAL MSY New Orleans LA
// States with the longest cumulative delays (with individual delays > 100 minutes) (origin: Seattle)
display(tripGraph.edges.filter($"src" === "SEA" && $"delay" > 100))
tripid delay src dst city_dst state_dst
3201938.0 108.0 SEA BUR Burbank CA
3201655.0 107.0 SEA SNA Orange County CA
1011950.0 123.0 SEA OAK Oakland CA
1021950.0 194.0 SEA OAK Oakland CA
1021615.0 317.0 SEA OAK Oakland CA
1021755.0 385.0 SEA OAK Oakland CA
1031950.0 283.0 SEA OAK Oakland CA
1031615.0 364.0 SEA OAK Oakland CA
1031325.0 130.0 SEA OAK Oakland CA
1061755.0 107.0 SEA OAK Oakland CA
1081330.0 118.0 SEA OAK Oakland CA
2282055.0 150.0 SEA OAK Oakland CA
3061600.0 130.0 SEA OAK Oakland CA
3170815.0 199.0 SEA DCA Washington DC null
2151845.0 128.0 SEA KTN Ketchikan AK
2281845.0 104.0 SEA KTN Ketchikan AK
3130720.0 117.0 SEA KTN Ketchikan AK
1011411.0 177.0 SEA IAH Houston TX
1022347.0 158.0 SEA IAH Houston TX
1021411.0 170.0 SEA IAH Houston TX
1031201.0 116.0 SEA IAH Houston TX
1031900.0 178.0 SEA IAH Houston TX
1042347.0 114.0 SEA IAH Houston TX
1062347.0 136.0 SEA IAH Houston TX
1101203.0 173.0 SEA IAH Houston TX
1172300.0 125.0 SEA IAH Houston TX
1250605.0 227.0 SEA IAH Houston TX
1291203.0 106.0 SEA IAH Houston TX
2141157.0 127.0 SEA IAH Houston TX
2150740.0 466.0 SEA IAH Houston TX
2180750.0 105.0 SEA IAH Houston TX
3010740.0 103.0 SEA IAH Houston TX
3021152.0 124.0 SEA IAH Houston TX
3121152.0 340.0 SEA IAH Houston TX
3140600.0 139.0 SEA IAH Houston TX
3171152.0 121.0 SEA IAH Houston TX
3280600.0 103.0 SEA IAH Houston TX
1151746.0 229.0 SEA HNL Honolulu, Oahu HI
1271746.0 111.0 SEA HNL Honolulu, Oahu HI
1030840.0 294.0 SEA HNL Honolulu, Oahu HI
2091035.0 132.0 SEA HNL Honolulu, Oahu HI
3141035.0 295.0 SEA HNL Honolulu, Oahu HI
3141930.0 128.0 SEA HNL Honolulu, Oahu HI
3311930.0 104.0 SEA HNL Honolulu, Oahu HI
3030840.0 185.0 SEA HNL Honolulu, Oahu HI
3240845.0 114.0 SEA HNL Honolulu, Oahu HI
1041740.0 256.0 SEA SJC San Jose CA
1061815.0 200.0 SEA SJC San Jose CA
3031600.0 161.0 SEA SJC San Jose CA
1031100.0 145.0 SEA LGB Long Beach CA
1041737.0 320.0 SEA LGB Long Beach CA
1081728.0 122.0 SEA LGB Long Beach CA
1221140.0 189.0 SEA LGB Long Beach CA
2121140.0 365.0 SEA LGB Long Beach CA
3070710.0 115.0 SEA LGB Long Beach CA
3180935.0 135.0 SEA LGB Long Beach CA
2141245.0 176.0 SEA RNO Reno NV
1052147.0 110.0 SEA BOS Boston MA
1081420.0 109.0 SEA BOS Boston MA
1112313.0 110.0 SEA BOS Boston MA
1232313.0 110.0 SEA BOS Boston MA
2140945.0 105.0 SEA BOS Boston MA
2032313.0 114.0 SEA BOS Boston MA
2121420.0 108.0 SEA BOS Boston MA
2141415.0 152.0 SEA BOS Boston MA
3282307.0 119.0 SEA BOS Boston MA
1110905.0 130.0 SEA EWR Newark NJ
1022227.0 236.0 SEA EWR Newark NJ
1180703.0 138.0 SEA EWR Newark NJ
2030905.0 212.0 SEA EWR Newark NJ
3141530.0 131.0 SEA EWR Newark NJ
3171530.0 181.0 SEA EWR Newark NJ
3202200.0 168.0 SEA EWR Newark NJ
1032115.0 196.0 SEA LAS Las Vegas NV
1201840.0 113.0 SEA LAS Las Vegas NV
1260840.0 165.0 SEA LAS Las Vegas NV
1261840.0 121.0 SEA LAS Las Vegas NV
1031905.0 103.0 SEA LAS Las Vegas NV
1041550.0 156.0 SEA LAS Las Vegas NV
1061820.0 213.0 SEA LAS Las Vegas NV
1061515.0 116.0 SEA LAS Las Vegas NV
1080805.0 235.0 SEA LAS Las Vegas NV
1170800.0 247.0 SEA LAS Las Vegas NV
2191235.0 210.0 SEA LAS Las Vegas NV
2281430.0 121.0 SEA LAS Las Vegas NV
2281235.0 187.0 SEA LAS Las Vegas NV
2170830.0 610.0 SEA LAS Las Vegas NV
2051205.0 110.0 SEA LAS Las Vegas NV
2111835.0 133.0 SEA LAS Las Vegas NV
2132005.0 135.0 SEA LAS Las Vegas NV
2272005.0 102.0 SEA LAS Las Vegas NV
3031430.0 108.0 SEA LAS Las Vegas NV
3141410.0 102.0 SEA LAS Las Vegas NV
3151205.0 103.0 SEA LAS Las Vegas NV
3281245.0 140.0 SEA LAS Las Vegas NV
3181520.0 103.0 SEA LAS Las Vegas NV
3292000.0 107.0 SEA LAS Las Vegas NV
1051955.0 160.0 SEA FAI Fairbanks AK
1040955.0 126.0 SEA DEN Denver CO
1040650.0 103.0 SEA DEN Denver CO
1160650.0 120.0 SEA DEN Denver CO
1011940.0 167.0 SEA DEN Denver CO
1041039.0 113.0 SEA DEN Denver CO
1041437.0 256.0 SEA DEN Denver CO
1041937.0 191.0 SEA DEN Denver CO
1040605.0 138.0 SEA DEN Denver CO
1061937.0 111.0 SEA DEN Denver CO
1121937.0 118.0 SEA DEN Denver CO
1171937.0 104.0 SEA DEN Denver CO
1021523.0 118.0 SEA DEN Denver CO
1041521.0 177.0 SEA DEN Denver CO
1061055.0 154.0 SEA DEN Denver CO
1281515.0 137.0 SEA DEN Denver CO
1011450.0 102.0 SEA DEN Denver CO
1021205.0 425.0 SEA DEN Denver CO
1031450.0 211.0 SEA DEN Denver CO
2210955.0 132.0 SEA DEN Denver CO
2111537.0 156.0 SEA DEN Denver CO
2110700.0 625.0 SEA DEN Denver CO
2191039.0 148.0 SEA DEN Denver CO
2211039.0 105.0 SEA DEN Denver CO
2031055.0 174.0 SEA DEN Denver CO
2051055.0 112.0 SEA DEN Denver CO
2211110.0 106.0 SEA DEN Denver CO
3131405.0 154.0 SEA DEN Denver CO
3181930.0 115.0 SEA DEN Denver CO
3191749.0 103.0 SEA DEN Denver CO
3011405.0 109.0 SEA DEN Denver CO
3121519.0 231.0 SEA DEN Denver CO
3061445.0 148.0 SEA DEN Denver CO
3181440.0 132.0 SEA DEN Denver CO
1011306.0 206.0 SEA IAD Washington DC null
1050806.0 105.0 SEA IAD Washington DC null
1052226.0 111.0 SEA IAD Washington DC null
1291256.0 108.0 SEA IAD Washington DC null
2031256.0 185.0 SEA IAD Washington DC null
2041256.0 129.0 SEA IAD Washington DC null
2101256.0 144.0 SEA IAD Washington DC null
2191316.0 122.0 SEA IAD Washington DC null
3080800.0 273.0 SEA IAD Washington DC null
3162225.0 174.0 SEA IAD Washington DC null
3201316.0 111.0 SEA IAD Washington DC null
3261311.0 104.0 SEA IAD Washington DC null
1111300.0 133.0 SEA PSP Palm Springs CA
1110910.0 171.0 SEA PSP Palm Springs CA
3170915.0 114.0 SEA PSP Palm Springs CA
3310645.0 179.0 SEA PSP Palm Springs CA
1161050.0 132.0 SEA SBA Santa Barbara CA
2091050.0 310.0 SEA SBA Santa Barbara CA
3191045.0 109.0 SEA SBA Santa Barbara CA
3241045.0 140.0 SEA SBA Santa Barbara CA
2122225.0 228.0 SEA CLT Charlotte NC
2142225.0 104.0 SEA CLT Charlotte NC
2152225.0 113.0 SEA CLT Charlotte NC
3081110.0 110.0 SEA CLT Charlotte NC
1290940.0 316.0 SEA ABQ Albuquerque NM
1171153.0 119.0 SEA PDX Portland OR
1171439.0 112.0 SEA PDX Portland OR
2091041.0 309.0 SEA PDX Portland OR
2090845.0 133.0 SEA PDX Portland OR
3021455.0 226.0 SEA PDX Portland OR
3021914.0 165.0 SEA PDX Portland OR
3090926.0 112.0 SEA PDX Portland OR
3251041.0 274.0 SEA PDX Portland OR
3261728.0 109.0 SEA PDX Portland OR
3301728.0 108.0 SEA PDX Portland OR
1112205.0 101.0 SEA MIA Miami FL
1262205.0 130.0 SEA MIA Miami FL
2142215.0 229.0 SEA MIA Miami FL
3292220.0 117.0 SEA MIA Miami FL
1012140.0 136.0 SEA SMF Sacramento CA
1010715.0 164.0 SEA SMF Sacramento CA
1021930.0 109.0 SEA SMF Sacramento CA
1031630.0 113.0 SEA SMF Sacramento CA
1041440.0 137.0 SEA SMF Sacramento CA
1041710.0 102.0 SEA SMF Sacramento CA
2211915.0 103.0 SEA SMF Sacramento CA
3262140.0 113.0 SEA SMF Sacramento CA
3271855.0 113.0 SEA SMF Sacramento CA
3191020.0 139.0 SEA SMF Sacramento CA
1291410.0 136.0 SEA PHX Phoenix AZ
1040830.0 294.0 SEA PHX Phoenix AZ
1300830.0 371.0 SEA PHX Phoenix AZ
1031510.0 119.0 SEA PHX Phoenix AZ
1061510.0 180.0 SEA PHX Phoenix AZ
1290720.0 147.0 SEA PHX Phoenix AZ
2082020.0 130.0 SEA PHX Phoenix AZ
2281855.0 186.0 SEA PHX Phoenix AZ
2110520.0 463.0 SEA PHX Phoenix AZ
2111132.0 107.0 SEA PHX Phoenix AZ
2160830.0 110.0 SEA PHX Phoenix AZ
2241132.0 107.0 SEA PHX Phoenix AZ
2251615.0 103.0 SEA PHX Phoenix AZ
3041455.0 108.0 SEA PHX Phoenix AZ
3051745.0 169.0 SEA PHX Phoenix AZ
3091455.0 126.0 SEA PHX Phoenix AZ
3251132.0 123.0 SEA PHX Phoenix AZ
3221530.0 121.0 SEA PHX Phoenix AZ
1060830.0 116.0 SEA DFW Dallas TX
1180830.0 132.0 SEA DFW Dallas TX
1281350.0 115.0 SEA DFW Dallas TX
1291545.0 247.0 SEA DFW Dallas TX
2031545.0 230.0 SEA DFW Dallas TX
2040830.0 135.0 SEA DFW Dallas TX
2061115.0 110.0 SEA DFW Dallas TX
2061545.0 125.0 SEA DFW Dallas TX
2061350.0 126.0 SEA DFW Dallas TX
2080830.0 356.0 SEA DFW Dallas TX
2090830.0 128.0 SEA DFW Dallas TX
3012320.0 123.0 SEA DFW Dallas TX
3152320.0 143.0 SEA DFW Dallas TX
3151400.0 146.0 SEA DFW Dallas TX
3301400.0 277.0 SEA DFW Dallas TX
1171220.0 110.0 SEA SFO San Francisco CA
1291220.0 103.0 SEA SFO San Francisco CA
1031125.0 107.0 SEA SFO San Francisco CA
1120924.0 268.0 SEA SFO San Francisco CA
1161058.0 131.0 SEA SFO San Francisco CA
1171058.0 138.0 SEA SFO San Francisco CA
1010955.0 104.0 SEA SFO San Francisco CA
1021914.0 105.0 SEA SFO San Francisco CA
1041830.0 131.0 SEA SFO San Francisco CA
1051214.0 139.0 SEA SFO San Francisco CA
1061214.0 384.0 SEA SFO San Francisco CA
1111310.0 124.0 SEA SFO San Francisco CA
1241310.0 133.0 SEA SFO San Francisco CA
1281310.0 250.0 SEA SFO San Francisco CA
1051855.0 166.0 SEA SFO San Francisco CA
2060955.0 148.0 SEA SFO San Francisco CA
2072125.0 105.0 SEA SFO San Francisco CA
2071845.0 203.0 SEA SFO San Francisco CA
2071220.0 139.0 SEA SFO San Francisco CA
2071100.0 113.0 SEA SFO San Francisco CA
2071405.0 144.0 SEA SFO San Francisco CA
2080955.0 121.0 SEA SFO San Francisco CA
2091835.0 124.0 SEA SFO San Francisco CA
2091405.0 101.0 SEA SFO San Francisco CA
2101220.0 134.0 SEA SFO San Francisco CA
2100955.0 107.0 SEA SFO San Francisco CA
2101100.0 105.0 SEA SFO San Francisco CA
2101405.0 105.0 SEA SFO San Francisco CA
2130955.0 108.0 SEA SFO San Francisco CA
2131100.0 139.0 SEA SFO San Francisco CA
2141100.0 107.0 SEA SFO San Francisco CA
2281100.0 130.0 SEA SFO San Francisco CA
2231058.0 136.0 SEA SFO San Francisco CA
2021310.0 115.0 SEA SFO San Francisco CA
2091820.0 149.0 SEA SFO San Francisco CA
2181526.0 106.0 SEA SFO San Francisco CA
2271905.0 154.0 SEA SFO San Francisco CA
2021450.0 139.0 SEA SFO San Francisco CA
2060950.0 150.0 SEA SFO San Francisco CA
2061450.0 140.0 SEA SFO San Francisco CA
2061855.0 119.0 SEA SFO San Francisco CA
2071855.0 146.0 SEA SFO San Francisco CA
2081330.0 164.0 SEA SFO San Francisco CA
2091450.0 106.0 SEA SFO San Francisco CA
2091855.0 182.0 SEA SFO San Francisco CA
2261450.0 259.0 SEA SFO San Francisco CA
2261855.0 224.0 SEA SFO San Francisco CA
2270950.0 174.0 SEA SFO San Francisco CA
2271450.0 240.0 SEA SFO San Francisco CA
2280950.0 207.0 SEA SFO San Francisco CA
2281450.0 331.0 SEA SFO San Francisco CA
2281855.0 124.0 SEA SFO San Francisco CA
3142043.0 101.0 SEA SFO San Francisco CA
3180950.0 155.0 SEA SFO San Francisco CA
3260950.0 117.0 SEA SFO San Francisco CA
3281430.0 112.0 SEA SFO San Francisco CA
3291050.0 138.0 SEA SFO San Francisco CA
3062055.0 113.0 SEA SFO San Francisco CA
3091028.0 143.0 SEA SFO San Francisco CA
3112055.0 116.0 SEA SFO San Francisco CA
3261043.0 121.0 SEA SFO San Francisco CA
3311043.0 257.0 SEA SFO San Francisco CA
3171237.0 182.0 SEA SFO San Francisco CA
3251933.0 197.0 SEA SFO San Francisco CA
3011330.0 115.0 SEA SFO San Francisco CA
3311045.0 189.0 SEA SFO San Francisco CA
3311440.0 101.0 SEA SFO San Francisco CA
1031152.0 397.0 SEA ATL Atlanta GA
1050830.0 106.0 SEA ATL Atlanta GA
1051152.0 107.0 SEA ATL Atlanta GA
1121159.0 201.0 SEA ATL Atlanta GA
1250630.0 206.0 SEA ATL Atlanta GA
1301159.0 117.0 SEA ATL Atlanta GA
1301322.0 179.0 SEA ATL Atlanta GA
2021159.0 145.0 SEA ATL Atlanta GA
2171320.0 133.0 SEA ATL Atlanta GA
3171320.0 109.0 SEA ATL Atlanta GA
1092015.0 119.0 SEA FAT Fresno CA
2012015.0 189.0 SEA FAT Fresno CA
2091150.0 232.0 SEA FAT Fresno CA
1021425.0 298.0 SEA ORD Chicago IL
1030600.0 103.0 SEA ORD Chicago IL
1081205.0 135.0 SEA ORD Chicago IL
1161205.0 582.0 SEA ORD Chicago IL
1241205.0 174.0 SEA ORD Chicago IL
1300815.0 209.0 SEA ORD Chicago IL
1021235.0 113.0 SEA ORD Chicago IL
1020830.0 151.0 SEA ORD Chicago IL
1051235.0 240.0 SEA ORD Chicago IL
1050830.0 163.0 SEA ORD Chicago IL
1241235.0 171.0 SEA ORD Chicago IL
1301235.0 111.0 SEA ORD Chicago IL
1300830.0 141.0 SEA ORD Chicago IL
1012359.0 227.0 SEA ORD Chicago IL
1040859.0 302.0 SEA ORD Chicago IL
1241110.0 223.0 SEA ORD Chicago IL
1311411.0 142.0 SEA ORD Chicago IL
2051235.0 115.0 SEA ORD Chicago IL
2050830.0 128.0 SEA ORD Chicago IL
2171235.0 204.0 SEA ORD Chicago IL
2170830.0 220.0 SEA ORD Chicago IL
2031615.0 185.0 SEA ORD Chicago IL
2171415.0 164.0 SEA ORD Chicago IL
2261415.0 138.0 SEA ORD Chicago IL
3120820.0 179.0 SEA ORD Chicago IL
3121200.0 151.0 SEA ORD Chicago IL
3200600.0 140.0 SEA ORD Chicago IL
3051235.0 140.0 SEA ORD Chicago IL
3120830.0 204.0 SEA ORD Chicago IL
3132240.0 127.0 SEA ORD Chicago IL
3162240.0 150.0 SEA ORD Chicago IL
3181417.0 127.0 SEA ORD Chicago IL
1091350.0 133.0 SEA MDW Chicago IL
1261350.0 109.0 SEA MDW Chicago IL
3171420.0 111.0 SEA MDW Chicago IL
3310600.0 206.0 SEA MDW Chicago IL
2271820.0 203.0 SEA COS Colorado Springs CO
3171825.0 205.0 SEA COS Colorado Springs CO
1250755.0 233.0 SEA JNU Juneau AK
1310755.0 210.0 SEA JNU Juneau AK
1311120.0 105.0 SEA JNU Juneau AK
3030755.0 110.0 SEA JNU Juneau AK
3130750.0 320.0 SEA JNU Juneau AK
1062320.0 107.0 SEA DTW Detroit MI
3121405.0 135.0 SEA ONT Ontario CA
3130725.0 174.0 SEA ONT Ontario CA
1171425.0 105.0 SEA LAX Los Angeles CA
1041700.0 264.0 SEA LAX Los Angeles CA
1051700.0 136.0 SEA LAX Los Angeles CA
1071645.0 151.0 SEA LAX Los Angeles CA
1311645.0 136.0 SEA LAX Los Angeles CA
1251020.0 130.0 SEA LAX Los Angeles CA
1261020.0 108.0 SEA LAX Los Angeles CA
1291258.0 126.0 SEA LAX Los Angeles CA
2022140.0 131.0 SEA LAX Los Angeles CA
2130610.0 135.0 SEA LAX Los Angeles CA
2091645.0 104.0 SEA LAX Los Angeles CA
2131645.0 134.0 SEA LAX Los Angeles CA
2031805.0 212.0 SEA LAX Los Angeles CA
2071805.0 105.0 SEA LAX Los Angeles CA
2071649.0 126.0 SEA LAX Los Angeles CA
2081649.0 154.0 SEA LAX Los Angeles CA
2091649.0 245.0 SEA LAX Los Angeles CA
2131705.0 107.0 SEA LAX Los Angeles CA
2161010.0 124.0 SEA LAX Los Angeles CA
2271149.0 192.0 SEA LAX Los Angeles CA
3141650.0 197.0 SEA LAX Los Angeles CA
3152105.0 115.0 SEA LAX Los Angeles CA
3171700.0 131.0 SEA LAX Los Angeles CA
3291700.0 118.0 SEA LAX Los Angeles CA
1050037.0 102.0 SEA MSP Minneapolis MN
1070700.0 193.0 SEA MSP Minneapolis MN
1130700.0 429.0 SEA MSP Minneapolis MN
2240655.0 109.0 SEA MSP Minneapolis MN
2121515.0 118.0 SEA MSP Minneapolis MN
1060800.0 132.0 SEA MCO Orlando FL
2220955.0 157.0 SEA SAN San Diego CA
3010955.0 108.0 SEA SAN San Diego CA
1031300.0 108.0 SEA ANC Anchorage AK
1062110.0 149.0 SEA ANC Anchorage AK
1132112.0 106.0 SEA ANC Anchorage AK
2072350.0 141.0 SEA ANC Anchorage AK
2091815.0 133.0 SEA ANC Anchorage AK
3181605.0 187.0 SEA ANC Anchorage AK
3231915.0 115.0 SEA ANC Anchorage AK
3311605.0 135.0 SEA ANC Anchorage AK
1022258.0 180.0 SEA JFK New York NY
1042258.0 285.0 SEA JFK New York NY
1022259.0 116.0 SEA JFK New York NY
2090715.0 110.0 SEA JFK New York NY
2022145.0 101.0 SEA JFK New York NY
2032145.0 165.0 SEA JFK New York NY
2031535.0 181.0 SEA JFK New York NY
2042145.0 201.0 SEA JFK New York NY
2142140.0 113.0 SEA JFK New York NY
2222140.0 118.0 SEA JFK New York NY
2032258.0 130.0 SEA JFK New York NY
2220700.0 404.0 SEA JFK New York NY
3310715.0 385.0 SEA JFK New York NY
3192140.0 119.0 SEA JFK New York NY
3091300.0 125.0 SEA JFK New York NY
1241000.0 806.0 SEA OGG Kahului, Maui HI
1030845.0 342.0 SEA PHL Philadelphia PA
1050845.0 174.0 SEA PHL Philadelphia PA
1210845.0 866.0 SEA PHL Philadelphia PA
1022215.0 121.0 SEA PHL Philadelphia PA
1031130.0 146.0 SEA PHL Philadelphia PA
1090835.0 148.0 SEA PHL Philadelphia PA
1170835.0 203.0 SEA PHL Philadelphia PA
2030845.0 202.0 SEA PHL Philadelphia PA
3130835.0 290.0 SEA PHL Philadelphia PA
1031810.0 142.0 SEA SLC Salt Lake City UT
1041016.0 117.0 SEA SLC Salt Lake City UT
1291725.0 111.0 SEA SLC Salt Lake City UT
1021555.0 175.0 SEA SLC Salt Lake City UT
1041825.0 110.0 SEA SLC Salt Lake City UT
2131635.0 134.0 SEA SLC Salt Lake City UT
2230710.0 739.0 SEA SLC Salt Lake City UT
2240710.0 477.0 SEA SLC Salt Lake City UT
2061005.0 119.0 SEA SLC Salt Lake City UT
3051315.0 123.0 SEA SLC Salt Lake City UT
3260710.0 149.0 SEA SLC Salt Lake City UT
3281750.0 125.0 SEA SLC Salt Lake City UT

Vertex Degrees

  • inDegrees: Incoming connections to the airport
  • outDegrees: Outgoing connections from the airport
  • degrees: Total connections to and from the airport

Reviewing the various properties of the property graph to understand the incoming and outgoing connections between airports.

// Degrees
// The number of degrees - the number of incoming and outgoing connections - for various airports within this sample dataset
display(tripGraph.degrees.sort($"degree".desc).limit(20))
id degree
ATL 179774.0
DFW 133966.0
ORD 125405.0
LAX 106853.0
DEN 103699.0
IAH 85685.0
PHX 79672.0
SFO 77635.0
LAS 66101.0
CLT 56103.0
EWR 54407.0
MCO 54300.0
LGA 50927.0
SLC 50780.0
BOS 49936.0
DTW 46705.0
MSP 46235.0
SEA 45816.0
JFK 43661.0
BWI 42526.0

City / Flight Relationships through Motif Finding

To more easily understand the complex relationship of city airports and their flights with each other, we can use motifs to find patterns of airports (i.e. vertices) connected by flights (i.e. edges). The result is a DataFrame in which the column names are given by the motif keys.

/*
Using tripGraphPrime to more easily display 
- The associated edge (ab, bc) relationships 
- With the different the city / airports (a, b, c) where SFO is the connecting city (b)
- Ensuring that flight ab (i.e. the flight to SFO) occured before flight bc (i.e. flight leaving SFO)
- Note, TripID was generated based on time in the format of MMDDHHMM converted to int
- Therefore bc.tripid < ab.tripid + 10000 means the second flight (bc) occured within approx a day of the first flight (ab)
Note: In reality, we would need to be more careful to link trips ab and bc.
*/
val motifs = tripGraphPrime.
  find("(a)-[ab]->(b); (b)-[bc]->(c)").
  filter("(b.id = 'SFO') and (ab.delay > 500 or bc.delay > 500) and bc.tripid > ab.tripid and bc.tripid < ab.tripid + 10000")

display(motifs)

Determining Airport Ranking using PageRank

There are a large number of flights and connections through these various airports included in this Departure Delay Dataset. Using the pageRank algorithm, Spark iteratively traverses the graph and determines a rough estimate of how important the airport is.

// Determining Airport ranking of importance using `pageRank`
val ranks = tripGraph.pageRank.resetProbability(0.15).maxIter(5).run()
ranks: org.graphframes.GraphFrame = GraphFrame(v:[id: string, City: string ... 3 more fields], e:[src: string, dst: string ... 5 more fields])
display(ranks.vertices.orderBy($"pagerank".desc).limit(20))
id City State Country pagerank
ATL Atlanta GA USA 18.910104616729814
DFW Dallas TX USA 13.699227467378964
ORD Chicago IL USA 13.163049993795985
DEN Denver CO USA 9.723388283811563
LAX Los Angeles CA USA 8.703656827807166
IAH Houston TX USA 7.991324463091128
SFO San Francisco CA USA 6.903242998287933
PHX Phoenix AZ USA 6.505886984498643
SLC Salt Lake City UT USA 5.799587684561128
LAS Las Vegas NV USA 5.25359244560915
SEA Seattle WA USA 4.626877547905697
EWR Newark NJ USA 4.401221169028188
MCO Orlando FL USA 4.389045874474043
CLT Charlotte NC USA 4.378459524081744
DTW Detroit MI USA 4.223377976049847
MSP Minneapolis MN USA 4.1490048912541795
LGA New York NY USA 4.129454491295321
BOS Boston MA USA 3.812077076528526
BWI Baltimore MD USA 3.53116352570383
JFK New York NY USA 3.521942669296845

BTW, A lot more delicate air-traffic arithmetic is possible for a full month of airplane co-trajectories over the radar range of Atlanta, Georgia, one of the busiest airports in the world.

See for instance:

Using the tripGraph, we can quickly determine what are the most popular single city hop flights

// Determine the most popular flights (single city hops)
import org.apache.spark.sql.functions._

val topTrips = tripGraph.edges.
  groupBy("src", "dst").
  agg(count("delay").as("trips"))
import org.apache.spark.sql.functions._
topTrips: org.apache.spark.sql.DataFrame = [src: string, dst: string ... 1 more field]
// Show the top 20 most popular flights (single city hops)
display(topTrips.orderBy($"trips".desc).limit(20))
src dst trips
SFO LAX 3232.0
LAX SFO 3198.0
LAS LAX 3016.0
LAX LAS 2964.0
JFK LAX 2720.0
LAX JFK 2719.0
ATL LGA 2501.0
LGA ATL 2500.0
LAX PHX 2394.0
PHX LAX 2387.0
HNL OGG 2380.0
OGG HNL 2379.0
LAX SAN 2215.0
SAN LAX 2214.0
SJC LAX 2208.0
LAX SJC 2201.0
ATL MCO 2136.0
MCO ATL 2090.0
JFK SFO 2084.0
SFO JFK 2084.0

Top Transfer Cities

Many airports are used as transfer points instead of the final Destination. An easy way to calculate this is by calculating the ratio of inDegree (the number of flights to the airport) / outDegree (the number of flights leaving the airport). Values close to 1 may indicate many transfers, whereas values < 1 indicate many outgoing flights and > 1 indicate many incoming flights. Note, this is a simple calculation that does not take into account of timing or scheduling of flights, just the overall aggregate number within the dataset.

// Calculate the inDeg (flights into the airport) and outDeg (flights leaving the airport)
val inDeg = tripGraph.inDegrees
val outDeg = tripGraph.outDegrees

// Calculate the degreeRatio (inDeg/outDeg), perform inner join on "id" column
val degreeRatio = inDeg.join(outDeg, inDeg("id") === outDeg("id")).
  drop(outDeg("id")).
  selectExpr("id", "double(inDegree)/double(outDegree) as degreeRatio").
  cache()

// Join back to the `airports` DataFrame (instead of registering temp table as above)
val nonTransferAirports = degreeRatio.as("d").join(airports.as("a"), $"d.id" === $"a.IATA").
  selectExpr("id", "city", "degreeRatio").
  filter("degreeRatio < 0.9 or degreeRatio > 1.1")

// List out the city airports which have abnormal degree ratios
display(nonTransferAirports)
id city degreeRatio
GFK Grand Forks 1.3333333333333333
FAI Fairbanks 1.1232686980609419
OME Nome 0.5084745762711864
BRW Barrow 0.28651685393258425
// Join back to the `airports` DataFrame (instead of registering temp table as above)
val transferAirports = degreeRatio.as("d").join(airports.as("a"), $"d.id" === $"a.IATA"). //degreeRatio.join(airports, degreeRatio("id") === airports("IATA")).
  selectExpr("id", "city", "degreeRatio").
  filter("degreeRatio between 0.9 and 1.1")
  
// List out the top 10 transfer city airports
display(transferAirports.orderBy("degreeRatio").limit(10))
id city degreeRatio
MSP Minneapolis 0.9375183338222353
DEN Denver 0.958025717037065
DFW Dallas 0.964339653074092
ORD Chicago 0.9671063983310065
SLC Salt Lake City 0.9827417906368358
IAH Houston 0.9846895050147083
PHX Phoenix 0.9891643572266746
OGG Kahului, Maui 0.9898718478710211
HNL Honolulu, Oahu 0.990535889872173
SFO San Francisco 0.9909473252295224

Breadth-first search (BFS) is designed to traverse the graph to quickly find the desired vertices (i.e. airports) and edges (i.e flights). Let's try to find the shortest number of connections between cities based on the dataset. Note, these examples do not take into account of time or distance, just hops between cities.

// Example 1: Direct Seattle to San Francisco
// This method returns a DataFrame of valid shortest paths from vertices matching "fromExpr" to vertices matching "toExpr"
val filteredPaths = tripGraph.bfs.fromExpr((col("id") === "SEA")).toExpr(col("id") === "SFO").maxPathLength(1).run()
display(filteredPaths)

As you can see, there are a number of direct flights between Seattle and San Francisco.

// Example 2: Direct San Francisco and Buffalo
// You can also specify expression as a String, instead of Column
val filteredPaths = tripGraph.bfs.fromExpr("id = 'SFO'").toExpr("id = 'BUF'").maxPathLength(1).run()
filteredPaths: org.apache.spark.sql.DataFrame = [id: string, City: string ... 2 more fields]
filteredPaths.show()
+---+----+-----+-------+
| id|City|State|Country|
+---+----+-----+-------+
+---+----+-----+-------+
display(filteredPaths) // display instead of show - same diference

But there are no direct flights between San Francisco and Buffalo.

// Example 2a: Flying from San Francisco to Buffalo
val filteredPaths = tripGraph.bfs.fromExpr("id = 'SFO'").toExpr("id = 'BUF'").maxPathLength(2).run()
display(filteredPaths)

But there are flights from San Francisco to Buffalo with Minneapolis as the transfer point.

Loading the D3 Visualization

Using the airports D3 visualization to visualize airports and flight paths

Warning: classes defined within packages cannot be redefined without a cluster restart.
Compilation successful.
d3a1.graphs.help()

Produces a force-directed graph given a collection of edges of the following form:
case class Edge(src: String, dest: String, count: Long)

Usage:
%scala
import d3._
graphs.force(
  height = 500,
  width = 500,
  clicks: Dataset[Edge])

// On-time and Early Arrivals
import d3a1._

graphs.force(
  height = 800,
  width = 1200,
  clicks = sql("select src, dst as dest, count(1) as count from departureDelays_geo where delay <= 0 group by src, dst").as[Edge])